## Friday, March 02, 2007

### What's special about this number?

0 is the additive identity.

1 is the multiplicative identity.

2 is the only even prime.

3 is the number of spatial dimensions we live in.

4 is the smallest number of colors sufficient to color all planar maps.

5 is the number of Platonic solids.

6 is the smallest perfect number.

7 is the smallest number of faces of a regular polygon that is not constructible by straightedge and compass.

8 is the largest cube in the Fibonacci sequence.

9 is the maximum number of cubes that are needed to sum to any positive

integer.

10 is the base of our number system.

11 is the largest known multiplicative persistence.

12 is the smallest abundant number.

13 is the number of Achimedian solids.

14 is the smallest number n with the property that there are no numbers relative prime to n smaller numbers.

15 is the smallest composite number n with the propert that there is only one group of order n.

16 is the only number of the form xy = yx with x and y different integers.

17 is the number of wallpaper groups.

18 is the only number that is twice the sum of its digits.

19 is the maximum number of 4th powers needed to sum to any number.

20 is the number f rooted trees with 6 vertices.

21 is the smallestnumber of distinct squares needed to tile a square.

22 is the number of partitions of 8.

23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.

24 is the largest number divisible by all numbers less tan its square root.

25 is the smallest square that can be written as a sum of 2 squares.

26 is theonly positive number to be directly between a square and a cube.

27 is the largest number that is the sum of the digits of its cube.

28 is the 2nd perfect number.

29 is the 7th Lucas number.

30 is the largest number with the property that all smaller numbers relatively prime to it are prime.

31 is a Mersenne prime.

32 is the smallest 5th power (besides 1).

33 is the largest number that is not a sum of distinct triangular numbers.

3 is the smallest number with the property that it and its neighbors have the same number of ivisors.

35 is the number of hexominoes.

36 is the smallest number (besides 1) which is both square and triangular.

37 is the maximum number o 5th powers needed to sum to any number.

38 is the last Roman numeral when written exicographically.

39 is the smallest number which has 3 different partitions into 3 parts with the same product.

40 is the only number whose letters are in alphabetical order.

41 is the smallest odd number that is not of the form | 2x - 3y |.

42 is the 5th Catalan number.

43 is the number of sided 7 diamonds.

4 is the number of derangements of 5 items.

45 is a Kaprekar number.

46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.

47 is the largest number f cubes that cannot tile a cube.

48 is the smallest number with 10 divisors.

49 is the smallest number with the property that it and its neighbors are squareful.

50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.

51 is the 6th Motzkin number.

52 is the 5th Bell number.

53 is the only two digit number that is reversed in hexadecimal.

54 is the smallest numbr that can be written as the sum of 3 squares in 3 ways.

55 is the largest triangular number in the Fibonacci sequence.

56 is the number of reduced 5×5 Latin squares.

57 = 111 in base .

58 is the number of commutative semigroups of order 4.

59 is the number of stellations of an icosahedron.

60 is the smallest number divisible by 1 through 6.

61 is the 6th Euler number.

62 is the smallest number that ca be written as the sum of of 3 distinct squares i 2 ways.

63 is the number of partially ordered sets of 5 elements.

64 is the smallest number with 7 divisors.

65 is the smallest number that becomes square if its reverse is either added to or subtrated from it.

66 is the number of 8-iamonds.

67 is the smallest number which is palindromic in bases 5 and 6.

68 is the 2-digit string that appars latest in the decimal expansion of π.

69 has the property that n2 and n3 together contain each digit once.

70 is the smallest abundant number that is not the sum ofsome subset of its divisors.

71 divides the sum of the primes less than it.

72 is the maximum number of spheres that can touch another sphere in a lattice packing in 6 dimnsions.

73 is the smallest number (besides 1) which is one less than twice its reverse.

74 is the number of different non-Hamiltonian polyhedra with minimum number of vertices.

75 is the nuber of orderings of 4 objects with ties allowed.

76 is an automorphic number.

77 is the largest number that cannot be written as a sum ofdistinct numbers whose reciprocals sum to 1.

78 is the smallest number that can be written as the sum of of 4 distinct squares in 3 ways.

79 is a permutableprime.

80 is the smallest number n where n and n+1 are both prodcts of 4 or moreprimes.

81 is the square of the sum of its digits.

82 is the number of 6-hexes.

83 is the number of zero-less pandigital squares.

84 is the largest order of a permutation of 14 elements.

85 is the largest n for which 12+22+32+...+n2 = 1+3+...+m has a solution.

86 = 222 in base 6.

87 is the sum of the squares of the first 4 primes.

88 is the only number known whose square has no isolated digits.

89 = 81 + 92

90 is the number of degrees in a right angle.

91 is the smallest pseudoprime in base 3.

92 is the number of different arrangements of 8 non-attacking queens on an

8×8 chessboard.

93 = 333 n base 5.

94 is a Smith number.

95 is the number of planar partitions of 10.

96 is the smallest number that can be written as the difference of 2 squares in 4 ways

97 s the smallest number with the property that its first 3 multiples contain the digit 9.

98 is the smallet number with the property that its first 5 multiples contain the digit 9.

99 is a Kaprekar number.

100 is the smallest square which is also the sum of 4 consective cubes.

101 is the number of partitions of 13.

102 is the smallest number with three different digits.

103 has the property that placing the last digit first gives 1 more than triple it.

104 is the smallest known number of unit line segments that can exist in the plane, 4 touching at every vertex.

05 is the largest number n known with the property that n - 2k is prime for k>1.

106 is the number of trees with 10 vertices.107 is the exponent of a Mersenne prime.

108 is 3 hyperfactorial.

109 is the smallest number which is palindromic n bases 5and 9.

110 is the smallest number that is the product of two different substrings.

111 is he smallest possible magic constant of a 3×3 magic square of distinct primes.112 is the side of the smallest square hat can be tiled with distinct integer-sided squares.

113 is a permutable prime.

11 = 222 in base 7.

115 is the number of rooted trees with 8 vertices.

116 is value of n for which n! + 1 is prime.

117 is the smallest possible value of the longest edge in a Heronian Tetrahedron.

118 is the smallest number that has 4 different partitions into 3 parts with the same product.

119 is the smallest number n were either n or n+1 is divisible by the numbers rom 1 to 8.

120 is the smallest number to appear 6 times in Pascal's triangle.

121 is the only square known of the form 1 + + p2 + p3 + p4, where p is prime.

122 is the smallest number n>1 so that n concatenated with n-1 0's concatenated with the reverse of n is prime.

123 is the 1th Lucas number.

124 is the smalles number with the property that its first 3 multiples contain the digit 2.

125 is the only number known that contains all its proper divisors as proper substrings.

126 = 9C4.

127 is a Mersenneprime.

128 is the largest number which is not the sum of distinct squares.

129 is the smallest number that can be ritten as he sum of 3 squares in 4 ways.

130 is the number of functions from 6 unlabeed points to themselves.

131 is a permutable prime.

132 is the smallest number which is the sum of al of the 2-digit numbers that can be formed with its digits.

133 is the smallest number n for which the sum of the proper divisors of n divides φ(n).

134 = 8C1 + 8C3 + 8C4.

135 = 11 + 32 + 53.

136 is the sum of the cubes of the digits of the sum of the cubes of its digits.

137 is the smallest prime with 3 distinct digits that remains prime if one of its digits is removed.

138 is the smallest possible product of 3 primes, one f which is the concatenation of the other tw.

139 is the number of unlabeled topologies with 5 elements.

140 is the smallest harmnic divisor number.

141 is a value of n such that the nth Cullen number is prime

142 is the number of planar graphs with 6 vertices.

143 is the smallest quasi-Carmichael number in base 8.

144 is the largest square in the Fibonacci seuence.

145 is a factorion.

146 = 222 in base 8.

147 is the number o sided 6-hexes.

148 is the number of perfect graphs with 6 vertices.

149 is the concatenationof the first 3 positive squares.

150 is the smallest n for which n + n times the nth prime is square.

151 is a palindromic prime.

152 has a square composed of the digits 0-4.

153 = 13 + 53 + 33.

154 is the smallest number which is palindromic in bases 6, 8, and 9.

155 is the sum of the primes betweenits smallest and largest prime factor.

156 is the numbr of graphs with 6 vertices.

157 is the largest number known whose square contais the same digits as its successor.

158 is the number of planar partitions of 11.

159 is the number of isoers of C11H24.

160 is the number of 9-iamonds.

161 is a Cullen number.

162 is the smallest number that can be written as the sum of of 4 positive squares n 9 ways.

163 is the largest Heegner Number.

164 is the smallest nmber which is the concatenation of squares in two different ways.

165 = 11C3.

166 is the number of mooton Boolean functions of 4 variables.

167 is the smallest number whose 4th power begins wit 4 identical digits

168 is the size of the smallest non-cyclic simple roup which is not an alternating group.

169 is the 7th Pell number.

170 is the smallest number n for which φ(n) and σ(n) are both square.

171 has the same nmber of digits in Roman numerals as its cube.

172 = 444 in base 6.

173 has a square containing only 2 digits.

174 is the smallest number tat can be written as the sum of of 4 positive

distinct squares in 6 ways.

175 = 11 + 7 + 53.

176 is an octagonal pentagonal number.

177 is the number of graphs with 7 edges.

178 has a cube with the same digits as anoher cube.

179 has a square comprised of the digits 0-4.

180 is the toal number of degrees in a triangle.

181 is a strobogrammatic prime.

182 is the number of connected bipartite grahs with 8 vertices.

183 is the smallest number n so tht n concatenated with n+1 is square.

184 is a Kaprekar constant in base 3.

185 s te number of conjugacy classes in the automorphism group of the 8 dimensional hypercube.

186 is th number of degree 11 irreducible polynomials over GF(2).

187 is th smallest quasi-Carmichael number in base 7.

188 is the number of semigroups of order 4.

189 is a Kaprekar constant in base 2.

190 is the largest number with theproperty that it and its distinct prime factors are palindromic in Roman numerals.

191 is a number n for which n, n+2, n+6, and n+8 are all prime.

192 is the smallest number with 14 divisors.

193 is the only known odd prime n for which 2 is not a primitive root of 4n2+1.

194 is the smallest number that can be written asthe sum of 3 squares in 5 ways.

195 is the smallest value of n such that 2nCn is divisible by n2.

196 is the smallest number that is not known to reach a palindrome when repeatedly added toits reverse.

197 is a Keith number.

198 = 11 + 99 + 88.

199 is the 11th Lucas number.

200 is the smallest numberwhich can not be mde prime by changing one of its digits.

201 is a Kaprekar constant in base 4.

202 has a cube that contains ony even digits.

203 is the 6th Bell number.

204 is the square root of a triangular number.

205 is the largest number which can not be writen as the sum of distinct primes of the form 6n+1.

206 is the smallest number that can be written as te sum of of 3 positive distinct squares in 5 ways.

207 has a 4th power where the first half of the digits are a permutation of the last half of the digits.

208 is the 10th tetranacci number.

209 is the smallest quasi-Carmichael number in base 9.

210 is the product of the first 4 primes.

211 has a cube containing only 3 different digits

212 has a square with 4/5 of the digts are the same.

213 is the number of perfct squared rectangles of order 13.

214 is a value of n for which n!! - 1 is prime.

215 = 555 in base 6.

216 is the smallest cube that can be written as the sum of 3 cubes.

217 is a Kaprekar constant in base 2.

218 is he number of digraphs with 4 vertices.

219 is thenumber of space groups, not including handedness.

220 is the smallest amicable number.

221 is the number of Hamiltonian planar graphs with 7 vertices.

222 is th number of lattices on 8 unlabeled nodes.

223 is the smallest prime which will nor remain prime if on of its digits is changed.

224 is not the sum of 4 non-zero squares.

225 is an octagonal square number.

226 ???

227 is the number of connected planar graphs with 8 edges.

228 = 444 in base 7.

229 is the smallest prime that remains prie when added to its reverse.

230 is the number of space groups, including handedness.

231 is the number of partitions of 16.

232 is the number of 7×7 symmetric permutation matrices.

233 is the smallest number with the property that it and its neighbors can be written as a sum of 2 squares.

234 ???

235 is the number of trees with 11 vertices.

236 is the numberof Hamiltonian circuits of a 4×8 rectangle.

237 is the smallest number with the roperty that its first 3 multiples contain the digit 7.

238 is the number of connected partial orders on 6 unlabeled elements.

239 is the largest number that cannot be written as a sum of 8 or fewer cubes.

240 is the smallest number with 20 divisors.

241 is the only number n for which the nth prime is π(n π(n)).

242 is the smallest n for which n, n+1, n+2, and n+3 have the same number of divisos.

243 = 35.

244 is the smallest number (besides 2) that can be written as the sum of 2 squares or the sum of 2 5th powers.

245 is a stella octangula number.

246 = 9C2 + 9C4 + 9C6.

247 is the smallest possible difference between two integers that together contain each digi exactly once.

248 is the smallest number n>1 for which the arithmetic, gometric, and harmonic means of φ(n) and σ(n) are all integers.

249 is the index of a prime Woodall number.

250 is the smallest ulti-digit number so that the sum of the suares of its prime factors equals te sum of the squares of its digits.

251 is the smallest number that can be written as the sum of 3 cubes in 2 ways.

252 is the 5th central binomial coefficient.

253 is the smallest non-trivial triangular star number.

254 is the smallest composite number all of whose ivisors (except 1) contain the digit 2.

255 = 11111111 in base 2.

256 is the smallest 8th power (besides 1).

257 is a Fermat prime.

258 is a value of n so tat n(n+9) is a palindrome.

259 = 1111 n base 6.

260 is the number of ways that 6 non-attacking bishops can be placed on a 4×4 chessboard.

261 is the umber of essentially different ways to dissect a 16-gon into 7 quadrilateral.

262 is the 5t meandric number and the 9th open meandric number.

263 is the largest nown prime whose square is strobogrammatic.

264 is the largest known number whose square is undulating.

265 is the number of derangements of 6 items.

266 is the Stirling number of the second kind S(8,6).

267 is the number of lanar partitions of 12.

268 is the smallest number whose product of digits is 6 imes the sum of its digits.

269 is the number of 6-octs.

270 is a harmonic divisor number.

271 is the smallest prime p so that p-1 and p+1 are divisible by cubes.

272 is the 7th Euler number.

273 = 333 in base 9.

274 is the Stirling number of the first kind s(6,2).

275 is the number of partitions of 28in which no part occurs only once.

276 is the sum of the first 3 5th powers.

277 is a Perrin number.

278 is the number of 3× sliding puzzle positions that reuire exactly 10 moves to solve starting with the hole on a side.

279 is the maximum number of 8th powers needed to sum to any number.

280 is the nmber of ways 18 people around a round table canshake hands in a non-crossing way, up to rotation.

281 is the sum of the first 14 primes.

282 is the number of planar partitions of 9.

283 = 25 + 8 + 35.

284 is an amicable number.

285 is the number of binary rooted trees with 13 vertices.

286 is the number of rooted trees with 9 vertices.

287 is the sum of cosecutive primes in 3 different ways.

288 is the smallest non-palindrome non-squae that when multiplied by its reverse is a square.

289 is a Friedman number.

290 has a base 3 representation that ends with its base 6 represntation.291 is the largest number that is not the sum of distinct integer powers

(larger than 1) of positive integers (larger than 1).

292 is th number of ways to make change for a dollar.

293 is the number of ways to hav one dollar in coins.

294 is the number of planar 2-connected graphs with7 vertices.

295 ???

296 is the number of partitions of 30 into distinct parts.

297 is a Kaprekar number.

298 is a value of n so that n(n+3) is a palindrome.

299 is the maximum number of regions a cube can be cu into with 12 cuts.

300 is the largest possible score in bowling.

301 is a 6-hyperperfect number.

302 is the number of acyclic digrahs with 5 vertices.

303 has a cube that is a concatenation of other cubes.

304 is a primitive semiperfect number.

305 is an hexagonal prism number.

306 is the number of 5-digit triangular numbers.

307 is a non-palindrome with a palindromic square.

308 is a heptagonal pyramidal number.

309 is smallest value of n for which σ (n-1) + σn+1) = σ(2n)

310 = 1234 in base 6.

311 is a permutable prime.

312 = 2222 in base 5.

313 is a palindromic prime.

314 is the smallest number that can be written as the sum of of 3 positive distinct squares in 6 ways.315 = (4+3)(4+1)(4+5).

316 has a digit product which is the digit sum of 316.

317 is a value of n for which one less than the product of the first n primes is prime.

318 is the number of unlabeled partially ordered ses of 6 lements.

319 is the smallest number with the property that the partition with the largest product does not have a maximum number of parts.

320 is the maximum determinant of a 10×10 matrix of 0's and 1's

321 is a Delannoy number.

322 is the 12th Lucas number.

323 is the product of twin prime.

324 is the largest possible product of positive integers with sum 16.

325 is a 3-hyperperfect number.

326 is the number of permutations of some subset of 5 elemnts.

327 and its double and triple together contain evry digit from 1-9 exactly once.

328 concatenated with its successor is square.

329 is a highly cototient number.

330 = 11C4.

331 is both a centered pentagonal number and a centered hexagonal number.

332 ???

333 is the number of 7-hexes.

334 is the number of trees on 13 vertices with diameter 7.

335 is the number of degree 12 irreducible polynmials over GF(2).

336 = 8P3.

337 is a permutable prime.

338 ???

339 ???

340 is a value f n for which n + 1 is prime.

341 is the smallest pseudoprime in base 2.

342 = 666 in base 7.

343 is a strong Friedman number.344 is thenumber of different arrangements of 4 non-attacking queens on a 4× chessboard.

345 is half again as large as the sum of its proper divisors.

346 is a Franel number.

347 is a Friedman number.

348 is the smallest number wose 5th power contains exactly the same digits as another 5th power.

349 is a tetranacci number.

350 is the Stirling number of the second knd S(7,4).

351 is the smallest number so that it and the surrounding numbers are all products of 4 or more primes.

352 is the number of different arrangements of 9 non-attacking queens on an 9×9 chessboard.

353 is the smallest number whose 4th power can be written as the sum of 4 4th pwers.

354 is the sum of the first 4 4th powers.

355 is the number of labeled topologes with 4 elements.

356 ???

357 has a base 3 representation that ends with its base 7 representation.

358 has a base 3 representation that ends with its base 7 representation.

359 has a base 3 representation that ends with its bae 7 representation.

360 is the number of degrees in a circle.

361 ??

362 and its double and triple ll use the same number of digits in Roman numerals.

363 ???

364 = 14C3.

365 is he smallest number that can be written as a sum of consecutive squares in more tha 1 way.

366 is the number of days in a leap year.

367 is the largest number whose square has strictly increasing digits.

368 is the number of ways to tile a 4×15 rectangle ith the pentominoes.

369 is the number of octominoes.

370 = 33 + 73 + 03.371 = 33 + 73 + 13

372 is a hexagonal pyramidal number.

373 is a permutable prime.

374 is the smallest number that can be written as the sum of 3 squares in 8 ways.

375 is a truncated tetrahedral number.

376 is an automorphic number.377 is the 14th Fibonacci number.

378 is the maximum number of regions a cube can be cu into with 13 cuts.

379 is a value of n for which one more than the product of the first n primes is prime.

380 ???

381 is a Kaprekar constant in base 2.

382 is the smallest number n with σ(n) = σ(n+3).

383 is the number of Hamiltonian graphs with 7 vertices.

384 = 8! = 12!!!!.

385 is the number of partitions of 18.

386 is the number of regions the complex plane is cut into by drawing lines between all pairs of 11th roots of unity.

387 ???

388 ???

389 ???

390 is the umberof partitions of 32 into distinct parts.

391 ???

392 is a Kaprekar constant in base 5.

393 ???

394 is a Schröder number.

395 ???

396 is the number of 3×3 sliding puzzle positions that require exactly 11 moves to solve starting with the hole in a corner.

397 is a Cuban prime.

398 ???

399 is a value of n for which n! + 1 is prime.

400 = 1111 in base 7.

401 is the nmber of connected planar Eulerian graphs with 9 vertices.

402 ???

403 is the product of two primes which are reverses of each other.

404 is the numbr of is the number of sided 10-hexes with holes.

405 is a pentagonal pyramidal number.

406 ???

407 = 43 + 03 + 73.

408 is the 8th Pell number.

409 ???

410 is the smallest number that can written as the sum of 2 distinct primes

in 2 ways.

411 is the number of triangles of any size contained in the triangle ofside

11 on a triangular grid.

412 ???

413 ???

414 ???

415 ???

416 ???

417 ???

418 ???

419 ???

420 is the smallest number divisible by 1 through 7.

421 ???

422 ???

423 ???

424 ???

425 ???

426 is a sella octangula number.

427 is a value of n for which n! + 1 is prime.

428 has theproperty that its square is the concatenation of two consecutive numbers.

429 is the 7th Catalan number.

430 ??

431 is the index of a prime Fibonacci number.

432 = (4) ()3 (2)2.

433 is the index of a prime Fibonacci number.

434 s the smallest composit value of n for which σ(n) + 2 = σ(n+2).

435 ???

436 ???

437 has a cube with the last 3 digits the same as the 3 digits before that.

438 = 666 in base 8.

439 is the smalest prime where inserting the same digit between every pair of digits never yields another prime.

440 ???

441 is the smallest square which is the sum of 6 consecutive cubes.

442 is the number of planar partitions of 13.

443 ???

444 is the largest known n for which there is a unique integer solution to a1+...+an=(a1)...(an).

445 has a base 10 representation which is the reverse of its base 9 representation.

446 is the smallest number that can be written as the sum of 3 distinct squares in 8 ways.

447 is the smallest number of convex quadrilaterals frmed by 15 points in general position.

448 is the number of 10-iamonds.

449 has a base 3 representation that begins with its base 7 representation.

450 is the number f 13-iamonds with holes.

451 is the smallest number whose reciprocal has period 10.

452 ???

453 ???

454 is the largest number known that cannot be witten as a sum of 7 or fewer cubes.

455 = 15C3.

456 is the numbr of tournaments with 7 vertices.

457 ???

458 ???

459 ???

460 ???

461 = 444 + 6 + 11.

462 = 11C5.

463 ???

464 is the maximum number of regions space can be divided into by 12 spheres.

465 is a Kaprekar constant in base 2.

466 = 1234 in base 7.

467 ha strictly increasing digits in bases 7, 9, and10.

468 = 3333 in base 5.

469 is the largest known value of n fr which n!-1 is prime.

470 has a base 3 representation that ends with its base 6 representation.

471 is the smallest number with the property that its first 4 multiples contain the digt 4.

472 is the number of 3×3 sliding puzzle positions that require exactly 29 move to solve starting with the hole in the center.

473 is the largest known number whose square and 4th power use differet digits.

474 ???

475 has a squae that is composed of overlapping squares of smaller numbers.

476 ???

477 ???

478 is the 7th Pell-Lucas number.

479 is the number of sets of distinct positive integers with mean 6.

480 is the smallest number which can be written as the difference f 2

squares in 8 ways.

481 is the number of conjugacy classes in the automorphism group of the dimensional hypercube

482 is a number whose square and cube use different diits.

483 is the last 3-digit string in the decimal expansion of π.

484 is a palindromic square number.

485 ???

486 is a Perrin numer.

487 is the number of Hadamard atrices of order 28.

489 is an octahedral number.

490 is the number of partitions of 19.

491 ???

492 is a hexanacci number.

493 ??

494 ???

495 is the Kaprekar constant for 3-digit numbers.

496 is the 3rd perfect number.

497 is the number of graphs with 8 edges.

499 is the smallest number with the property that its first 12 multiples contain the digit 9.

500 is the number of planar partitios of 10.

501 is the number of partitions of 5 items into ordered lists.

502 uses the same digits as φ(502).

503 is the smallest prime which is the sum of the cubes of the first few

pries.

504 = 9P3.

505 = 10C5 + 10C0 + 10C5.

506 is the sum of the first 11 squares.

509 is the index of a prime Fibonacci number.

510 is the number f binary rooted trees with 14 vertices.

511 = 111111111 in base 2.

512 is the cube of the sum of its digits.

515 is the number of graphs on6 vertices with no isolated vertices.

516 is the number of partitions of 32 in which no part occurs only once.

518 = 51 + 12 + 83.

519 is the number of trees on 15 vertices with diameter 5.

520 is thenumber of ways to place non-attacking kings on a 6×6

chessboard.

521 is the 13th Lucas umber.

522 is the number of ways to place a non-attacking white and black paw on a

6×6 chessboard.

524 is the number of 6-kings.

525 is a hexagonal pyramidal number.

527 is the smallest number nfor which theredo not exist 4 smaller numbers

so that a1! a2! a3! a4! n! is square.

528 concatenated with its successor is square.

530 is the sum of the first 3 perfect numbers.

531 is the smallest number with the property that its first 4 mltiples

contain the digit 1.

535 is a palindrome whose φ(n) is also palindromic.

536 is the number of solutions of the stomachin puzzle.

538 is the 10th open meandric number.

539 is the number of multigraphs wth 5 vertices and 9 edgs.

540 is divisible by its reverse.

541 is the number of orderings of 5objects with ties allowed.

543 is a number whose square and ube use different digits.

545 has a base 3 representation that begins with its base 4 representation.

546 undulates in bases 3, 4, and 5.

547 is a Cban prime.

548 is the maximum number of 9th powers needed to sum to any number.

550 is a pentagonal pyramidal number.

551 is the number of trees with 12 vertices.

552 is the number of prime knots with 11 crossings.

554 is the number of self-dual planar graphs with 20 edges.

555 is a repigit.

558 divides the sum of he largest prime factors of the first 558 positive

integers.

559 is a centered cube number.

560 = 16C3.

561 i the smallest Carmichael number.

563 is the largest known Wilson prime.

567 has the poperty that it and its square toether use the digits 1-9

once.

568 is the smallest number whose 7th power can be written as the sum of 7

7th powers.

569 is the smallest number n for which th concatenation of n, (n+1), ...

(n+30) is prime.

570 is the product f all the prime palindromic Roman numerals.

571 is the index of a prime Fibonacci number.

572 is the smallest number which has equal numbers of every digit in bses 2

and 3

573 has the property that its square is the concatenation of two consecutive

numbers.

574 is the mximum number of pieces a torus can be cut into with 14 cuts.

575 is a palindrome that is one less than a square.

576 is the number of 4×4 Latin squares.

581 has a base 3 representation that begins with ts base 4 representation.

582 is the numbe of antisymmetric relations on a 5 element set.

583 is the smallest number whose reciprocal has period 26.

585 = 1111 in bse 8.

586 is the smallest number that appears in its factorial 6 times

587 is the smallest number whose sum of dgits is larger than that of its

cube.

588 is the number of possible rook moves on a 7×7 chessboard.

592 evenly divides the sum of its rotations.

593 is a Leyland number.

594 = 15 + 29 + 34.

55 is a palindromic triangular number.

596 is the number of Hamiltonian cycles of a 4×9 rectangle graph.

598 = 51 + 92 + 83.

602 is the umber of lattice points that are within 1/2 of a sphere of

radius 7 centered at the origin.

604 and the two numbers before it and after it are all products of exactly 3

primes.

607 is the exponent of a Mersenne prime.

610 is the smallest Fibonacci number that begins with 6.

612 is a number whose square and cube use different digits.

614 is the smallest number that can be written as the sum of 3 squares in 9

ways.

615 = 555 + 55 + 5.

616 is a Padovan number.

617 = 1!2 + 2!2 + 3!2 + 4!2.

61 is the number of ternary square-free words of length 15.

619 is a strobogrammatic prime.

620 is the number of sided 7-hexes.

621 is the number of ways to9-color the faces of a tetrahedron.

624 is the smallest number with the property that ts first 5 multiples

contain the digit 2.

625 is an automorphic number.

627 is the number of partitions of 20.

629 evenly divides the sum of its rotations.

630 is the number of degree 13 irreducible polynomials over GF(2).

631 has a base 2 representation tht begins with its base 5 representation.

637 = 777 in base 9.

638 is the number of fixed 5-kings.

641 is the smallest prime factor of 225+1.

642 is the smallest number with the property that its first 6 mltiples

contain the digit 2.

643 is the largest prime factor of 123456.

644 is a Perrin number.

645 is the largest n for which 1+2+3+...+n = 12+22+32+...+k2 for some k.

646 is the number of connected planar graphs with 7 vertices.

648 is the smallest number whose decimal part of its 6th root begins with a

permutation of the digits 1-9.

650 is the sum of the first 12 squares.

651 is an nonagonal entagonal number.

652 is the only known non-perfect number whose number of divisors and sum of

smaller divisors are perfect.

653 is the only known prime for which 5 is neither a primitive root or a

quadratic residue of 4n2+1.

658 is the number of triangles of any size contained in the triangle of side

13 on a triangular grid.

660 is the order of a non-cyclic simple group.

664 is a value of n so that n(n+7) is a palindrome.

666 is the largest rep-digit triangular number.

667 is the product of two consecutive primes.

668 i the number of legal pawn moves in chess.

670 is an octahedral number.

671 is a rhombic doecahedral number.

672 is a multi-perfect number.

673 is a tetranacci number.

675 is the smallest order for which there are 17 groups.

676 is the smallest palindromic square number whose square root is not

palindromic.

679 is the smallest number with multiplicative persistence 5.

680 is the smallest tetrahedral number that is also the sum of 2 tetrahedral

numbers.

682 = 11C6 + 11C8 + 11C2.

683 is a Wagstaff prime.

686 is the number of partitions of 35 in which no part occurs only once.

688 is a Friedman number.

689 is the smallest number that can be written as the sumof 3 distinct

squares in 9 ways.

694 is the number of different arrangements (up to rotation and reflection)

of 7 non-attacking rooks on a 7×7 chessboard.

695 is themaximum number of pieces a torus can be cut into with 15 cuts.

696 is a palindrome n sothat n(n+8) is also palindromic.

697 is a 12-hyperperfect number.

700 is the number of symmetric 8-cubes.

703 is a Kaprekar number.

704 is the number of sided octominoes.

707 is the smallest number whose reciprocal has period12.

709 is the number of connected planar graphs with 9 edges.

710 is the number of connected graphs with 9 edges.

712 uses the same digits as π(712).

714 is the smallest number which has equal numbers of every digit in bases 2

and 5.

715 = 13C4.

718 is the number of unlabeled topologies with 6 elements.

719 is the number of rooted trees with 10 vertices.

720 = 6!

721 is the smallest number which can be written as the difference of two

cubes in 2 ways.

724 is the number of different arrangements of 10 non-attacking queens on an

10×10 chessboard.

726 is a pentagonal pyramidal number.

727 has the property that its square is the concatenation of two consecutive

numbers.

728 is the smallest number n where n and n+1 are both products of 5 or more

primes.

729 = 36.

730 is the number of connected bipartite graphs with 9 vertices.

731 is the number of planar partitions of 14.

732 = 17 + 26 + 35 + 44 + 53 + 62 + 71.

733 is the sum of the digits of 444.

734 is the smallest number that can be written as the sum of 3 distinct

non-zero squares in 10 ways.

735 is the smallest number that is the concatenation of its distinct prime

factors.

736 is a strong Friedman number.

739 has a base 2 representation that begins with its base 9 representation.

740 is the number of self-avoiding walks of length 8.

741 is the number of multigraphs with 6 vertices and 8 edges.

742 is the smallest number that is one more than triple its reverse.

743 is the number of independent sets of the graph of the 4-dimensional

hypercube.

744 is the number of perfect squared rectangles of order 14.

746 = 17 + 24 + 36.

748 is the number of 3×3 sliding puzzle positions that require exactly 12

moves to solve starting with the hole in a corner.

750 is the Stirling number of the second kind S(10,8).

751 is the index of a prime Woodall number.

752 is the number of conjugacy classes in the automorphism group of the 11

dimensional hypercube.

755 is the number of trees on 14 vertices with diameter 6.

756 is the maximum number of regions space can be divided into by 14

spheres.

757 is the smallest number whose reciprocal has a period of 27.

760 is the number of partitions of 37 into distinct parts.

762 is the first decimal digit of π where a digit occurs four times in a

row.

764 is the number of 8×8 symmetric permutation matrices.

765 is a Kaprekar constant in base 2.

767 is the largest n so that n2 = mC0 + mC1 + mC2 + mC3 has a solution.

769 is the total number of digits of all binary numbers of length 1-7.

773 is the smallest odd number n so that n+2k is composite for all k<n.

777 is a repdigit in bases 6 and 10.

780 = (5+7)(5+8)(5+0).

781 = 11111 in base 5.

782 is a number whose sum of divisors is a 4th power.

784 is the sum of the first 7 cubes.

786 is the largest known n for which 2nCn is not divisible by the square of

an odd prime.

787 is a palindromic prime.

788 is the smallest of 6 consecutive numbers divisible by 6 consecutive

primes.

789 is the largest 3-digit number with increasing digits.

791 is the smallest number n where either it or its neighbors are divisible

by the numbers from 1 to 12.

792 is the number of partitions of 21.

793 is one less than twice its reverse.

794 is the sum of the first three 6th powers.

795 is a number whose sum of divisors is a 4th power.

797 is the number of functional graphs on 9 vertices.

798 is the number of ternary square-free words of length 16.

800 = 2222 in base 7.

802 is the number of isomers of C13H28.

804 is a value of n for which 2φ(n) = φ(n+1).

810 is the number of necklaces with 8 white and 8 black beads.

812 is the number of triangles of any size contained in the triangle of side

14 on a triangular grid.

814 is a value of n so that n(n+5) is a palindrome.

816 = 18C3.

819 is the smallest number so that it and its successor are both the product

of 2 primes and the square of a prime.

820 = 1111 in base 9.

821 is a number n for which n, n+2, n+6, and n+8 are all prime.

822 is the number of planar graphs with 7 vertices.

832 is the maximum number of pieces a torus can be cut into with 16 cuts.

834 is the maximum number of regions a cube can be cut into with 17 cuts.

835 is the 9th Motzkin number.

836 is a non-palindrome with a palindromic square.

839 has a base 5 representation that begins with its base 9 representation.

840 is the smallest number divisble by 1 through 8.

841 is a square that is also the sum of 2 consecutive squares.

842 is a value of n for which n!! - 1 is prime.

843 is the 14th Lucas number.

844 is the smallest number so that it and the next 4 numbers are all

squareful.

846 has the property that its square is the concatenation of two consecutive

numbers.

849 is a value of n for which σ(n-1) = σ(n+1).

850 is the number of trees on 14 vertices with diameter 7.

853 is the number of connected graphs with 7 vertices.

854 has the property that it and its square together use the digits 1-9

once.

855 is the smallest number which is the sum of 5 consecutive squares or 2

consecutive cubes.

857 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

858 is the smallest palindrome with 4 different prime factors.

859 is the number of planar partitions of 11.

862 is a number whose sum of divisors is a 4th power.

863 is a value of n so that n(n+6) is a palindrome.

864 is the number of partitions of 38 into distinct parts.

866 is the number of sided 10-iamonds.

868 has a square root whose decimal part starts with the digits 1-9 in some

order.

870 is the sum of its digits and the cube of its digits.

872 is a value of n for which n! + 1 is prime.

873 = 1! + 2! + 3! + 4! + 5! + 6!

877 is the 7th Bell number.

878 is the number of 3×3 sliding puzzle positions that require exactly 29

moves to solve starting with the hole on a side.

880 is the number of 4×4 magic squares.

888 and the following 18 numbers are composite.

889 is a Kaprekar constant in base 2.

891 is an octahedral number.

894 has a base 5 representation that begins with its base 9 representation.

895 is a Woodall number.

896 is not the sum of 4 non-zero squares.

897 is a Cullen number.

899 is the product of twin primes.

900 has a base 5 representation that begins with its base 9 representation.

901 is the sum of the digits of the first 100 positive integers.

902 is a value of n so that n(n+7) is a palindrome.

906 is the number of perfect graphs with 7 vertices.

907 is the largest n so that Q(√n) has class number 3.

909 is a value of n that has has no digits in common with 2n, 3n, 4n, 5n,

6n, 7n, 8n, or 8n.

912 is a Pentanacci number.

913 has exactly the same digits in 3 different bases.

914 is the number of binary rooted trees with 15 vertices.

919 is the smallest number which is not the difference between palindromes.

922 = 1234 in base 9.

924 is the 6th central binomial coefficient.

925 is the number of partitions of 37 in which no part occurs only once.

927 is the 13th tribonacci number.

929 is a palindromic prime.

935 is a number whose sum of divisors is a 4th power.

936 is a pentagonal pyramidal number.

939 has a cube root whose decimal part starts with the digits 1-9 in some

order.

940 is the maximum number of regions space can be divided into by 15

spheres.

941 is the smallest number which is the reverse of the sum of its proper

substrings.

945 is the smallest odd abundant number.

946 is a hexagonal pyramidal number.

948 is the number of symmetric plane partitions of 24.

951 is the number of functions from 8 unlabeled points to themselves.

952 = 93 + 53 + 23 + (9)(5)(2).

953 is the largest prime factor of 54321.

957 is a value of n for which σ(n) = σ(n+1).

960 is the sum of its digits and the cube of its digits.

961 is a square whose digits can be rotated to give another square.

964 is the number of 3×3 sliding puzzle positions that require exactly 12

moves to solve starting with the hole in the center.

966 is the Stirling number of the second kind S(8,3).

967 is the number of 6-digit triangular numbers.

969 is a tetrahedral palindrome.

974 is the number of multigraphs with 5 vertices and 10 edges.

976 has a square formed by inserting a block of digits inside itself.

979 is the sum of the first 5 4th powers.

981 is the smallest number that has 5 different partitions into 3 parts with

the same product.

982 is the number of partitions of 39 into distinct parts.

985 is the 9th Pell number.

986 = 19 + 28 + 36.

987 is the 16th Fibonacci number.

988 is the maximum number of regions a cube can be cut into with 18 cuts.

990 is a triangular number that is the product of 3 consecutive integers.

991 is a permutable prime.

992 is the number of differential structures on the 11-dimensional

hypersphere.

993 is the number of paraffins with 8 carbon atoms.

994 is the smallest number with the property that its first 18 multiples

contain the digit 9.

995 has a square formed by inserting a block of digits inside itself.

996 has a square formed by inserting a block of digits inside itself.

997 is the smallest number with the property that its first 37 multiples

contain the digit 9.

998 is the smallest number with the property that its first 55 multiples

contain the digit 9.

999 is a Kaprekar number.

1000 = 103.

1001 is the smallest palindromic product of 3 consecutive primes.

1002 is the number of partitions of 22.

1003 has a base 2 representation that ends with its base 3 representation.

1004 is a heptanacci number.

1005 is the smallest number whose English name contains all five vowels

exactly once.

1006 has a cube that is a concatenation of other cubes.

1009 is the smallest number which is the sum of 3 distinct positive cubes in

2 ways.

1010 is the number of ways to tile a 5×12 rectangle with the pentominoes.

1011 has a square that is formed by inserting three 2's into it.

1012 has a square that is formed by inserting three 4's into it.

1015 is the sum of the first 14 squares.

1016 is a stella octangula number.

1019 is a value of n for which one more than the product of the first n

primes is prime.

1020 is the number of ways to place 2 non-attacking kings on a 7×7

chessboard.

1021 is a value of n for which one more than the product of the first n

primes is prime.

1022 is a Friedman number.

1023 is the smallest number with 4 different digits.

1024 is the smallest number with 11 divisors.

1025 is the smallest number that can be written as the sum of a square and a

cube in 4 ways.

1029 is the smallest order for which there are 19 groups.

1031 is the length of the largest repunit that is known to be prime.

1032 is the smallest number that can be written as the sum of a cube and a

fifth power in more than one way.

1033 = 81 + 80 + 83 + 83.

1035 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

1036 = 4444 in base 6.

1037 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

1039 is the largest known number n so that 96n - 95n is prime.

1044 is the number of graphs with 7 vertices.

1045 is an octagonal pyramidal number.

1050 is the Stirling number of the second kind S(8,5).

1052 has the property that placing the last digit first gives 1 more than

twice it.

1056 is the area of the smallest non-square rectangle that can be tiled with

integer-sided squares.

1066 is a value of n for which 2φ(n) = φ(n+1).

1067 has exactly the same digits in 3 different bases.

1072 is the smallest number that can be written as the sum of 2, 3, 4, or 5

cubes.

1078 is the number of lattices on 9 unlabeled nodes.

1079 is the smallest number n where either it or its neighbors are divisible

by the numbers from 1 to 15.

1080 is the smallest number with 18 divisors.

1081 is a triangular number that is the product of two primes.

1084 is the smallest number whose English name contains all five vowels in

order.

1086 is the number of 13-hexes with reflectional symmetry.

1089 is one ninth of its reverse.

1091 is the largest known number n so that 73n - 72n is prime.

1092 is the order of a non-cyclic simple group.

1093 is the smallest Wieferich prime.

1095 is the number of vertices in a Sierpinski triangle of order 6.

1097 is the closest integer to e7.

1098 = 11 + 0 + 999 + 88.

1099 = 1 + 0 + 999 + 99.

1100 has a base 3 representation that ends with 1100.

1101 has a base 2 representation that ends with 1101.

1104 is a Keith number.

1105 is a rhombic dodecahedral number.

1111 is a repdigit.

1112 has a base 3 representation that begins with 1112.

1113 is the number of partitions of 40 into distinct parts.

1116 is the number of 8-abolos.

1122 = 33C1 + 33C1 + 33C2 + 33C2.

1123 has digits which start the Fibonacci sequence.

1124 is a Leyland number.

1128 is an icosahedral number.

1130 is a Perrin number.

1139 has the property that placing the last digit first gives 1 more than 8

times it.

1140 is the smallest number whose divisors contain every digit at least

three times.

1141 is the smallest number whose 6th power can be written as the sum of 7

6th powers.

1142 is the number of ways to place a non-attacking white and black pawn on

a 7×7 chessboard.

1147 is the product of two consecutive primes.

1148 is the number of ways to fold a strip of 9 stamps.

1151 is the largest known number n so that 6n - 5n is prime.

1152 is a highly totient number.

1153 is the smallest number with the property that its first 3 multiples

contain the digit 3.

1154 is the 8th Pell-Lucas number.

1155 is the product of 4 consecutive primes.

1156 is a square whose digits are non-decreasing.

1158 is the maximum number of pieces a torus can be cut into with 18 cuts.

1160 is the maximum number of regions a cube can be cut into with 19 cuts.

1161 is the number of degree 14 irreducible polynomials over GF(2).

1165 is the number of conjugacy classes in the automorphism group of the 12

dimensional hypercube.

1166 is a heptagonal pyramidal number.

1167 is the smallest number whose 8th power can be written as the sum of 9

8th powers.

1170 = 2222 in base 8.

1171 has a 4th power containing only 4 different digits.

1130 and the following 20 numbers are composite.

1177 is a number whose sum of divisors is a 4th power.

1181 is the largest known number n so that 34n - 33n is prime.

1183 is the smallest number with the property that its first 4 multiples

contain the digit 3.

1184 is an amicable number.

1185 = 11 + 1111 + 8 + 55.

1186 is the number of 11-iamonds.

1187 = 111 + 111 + 888 + 77.

1188 is the number of triangles of any size contained in the triangle of

side 16 on a triangular grid.

1189 is the square root of a triangular number.

1191 is the number of symmetric plane partitions of 25.

1193 and its reverse are prime, even if we append or prepend a 3 or 9.

1197 is the smallest number that contains as substrings the maximal prime

powers that divide it.

1200 = 3333 in base 7.

1201 has a square that is formed by inserting three 4's into it.

1203 is the smallest number n for which the concatenation of n, (n+1), ...

(n+34) is prime.

1206 is a Friedman number.

1207 is the product of two primes which are reverses of each other.

1210 is an amicable number.

1214 is a number whose product of digits is equal to its sum of digits.

1215 is the smallest number n where n and n+1 are both products of 6 or more

primes.

1219 is a number whose sum of divisors is a 4th power.

1222 is a hexagonal pyramidal number.

1224 is the smallest number that can be written as the sum of 4 cubes in 3

ways.

1225 is a hexagonal square triangular number.

1229 is the number of primes less than 10000.

1230 has the property that 17 + 27 + 37 + 07 equals 1230 written in base 8.

1231 has the property that 17 + 27 + 37 + 17 equals 1230 written in base 8.

1233 = 122 + 332.

1234 is the smallest 4-digit number with increasing digits.

1240 is the sum of the first 15 squares.

1241 is a centered cube number.

1243 is the number of essentially different ways to dissect a 18-gon into 8

quadrilaterals.

1246 is the number of partitions of 38 in which no part occurs only once.

1248 is the smallest number with the property that its first 6 multiples

contain the digit 4.

1249 is the number of simplicial polyhedra with 11 vertices.

1250 is the number of lattice points that are within 1/2 of a sphere of

radius 10 centered at the origin.

1255 is a Friedman number.

1257 is a value of n for which φ(σ(n)) = φ(n).

1260 is the smallest number with 36 divisors.

1275 has a square that is formed by 3 squares that overlap by 1 digit.

1276 = 1111 + 22 + 77 + 66.

1278 has a square root whose decimal part starts with the digits 1-9 in some

order.

1279 is the exponent of a Mersenne prime.

1285 is the number of 9-ominoes.

1287 = 13C5.

1292 is a factor of the sum of the digits of 12921292.

1294 is the number of 4 dimensional polytopes with 8 vertices.

1295 = 5555 in base 6.

1296 is a Friedman number.

1297 is a tetranacci number.

1298 has a base 3 representation that ends with its base 6 representation.

1300 is the sum of the first 4 5th powers.

1301 is the number of trees with 13 vertices.

1302 is the number of trees on 17 vertices with diameter 5.

1303 is the number of multigraphs with 7 vertices and 8 edges.

1306 = 11 + 32 + 03 + 64.

1307 is the largest known number n so that 97n - 96n is prime.

1310 is the smallest number so that it and its neighbors are products of

three primes.

1320 = 12P3.

1328 and the following 32 numbers are composite.

1330 = 21C3.

1331 is a cube containing only odd digits.

1332 has a base 2 representation that begins and ends with its base 6

representation.

1333 has a base 2 representation that ends with its base 6 representation.

1334 is a value of n for which σ(n) = σ(n+1).

1348 is the number of 3×3 sliding puzzle positions that require exactly 13

moves to solve starting with the hole on a side.

1349 is the maximum number of pieces a torus can be cut into with 19 cuts.

1351 is the maximum number of regions a cube can be cut into with 20 cuts.

1352 is an hexagonal prism number.

1357 has digits in arithmetic sequence.

1364 is the 15th Lucas number.

1365 = 15C4.

1366 = 1 + 33 + 666 + 666.

1368 is the number of ways to fold a 3×3 rectangle of stamps.

1369 is a square whose digits are non-decreasing.

1370 = 12 + 372 + 02.

1371 = 12 + 372 + 12.

1376 is the smallest number with the property that it and its neighbors are

not cubefree.

1385 is the 8th Euler number.

1386 = 1 + 34 + 8 + 64.

1392 is the number of ternary square-free words of length 18.

1393 is an NSW number.

1394 is the maximum number of regions space can be divided into by 17

spheres.

1395 is a vampire number.

1400 is the number of different arrangements of 4 non-attacking queens on a

4×10 chessboard.

1405 is the sum of consecutive squares in 2 ways.

1408 is the number of symmetric 3×3 matrices in base 4 with determinant 0.

1409 is a prime factor of 11111111111111111111111111111111.

1412 has a cube whose digits occur with the same frequency.

1413 is the number of triangles of any size contained in the triangle of

side 17 on a triangular grid.

1416 is the number of connected planar maps with 6 edges.

1419 is a Zeisel number.

1421 is a number whose product of digits is equal to its sum of digits.

1426 is the number of partitions of 42 into distinct parts.

1429 is the smallest number whose square has the first 3 digits the same as

the next 3 digits.

1430 is the 8th Catalan number.

1432 is a Padovan number.

1434 is a number whose sum of squares of the divisors is a square.

1435 is a vampire number.

1444 is a square whose digits are non-decreasing.

1448 is the number of 8-hexes.

1449 is a stella octangula number.

1452 is a value of n so that n(n+4) is a palindrome.

1453 = 1111 + 4 + 5 + 333.

1454 = 11 + 444 + 555 + 444.

1455 is the number of subgroups of the symmetric group on 6 symbols.

1456 is the number of regions formed when all diagonals are drawn in a

regular 15-gon.

1458 is the maximum determinant of a 11×11 matrix of 0's and 1's.

1459 = 11 + 444 + 5 + 999.

1465 has a square that is formed by inserting three 2's into it.

1467 has the property that eπ√1467 is within 10-8 of an integer.

1469 is an octahedral number.

1470 is a pentagonal pyramidal number.

1471 is the number of regions the complex plane is cut into by drawing lines

between all pairs of 15th roots of unity.

1476 is the number of graphs with 9 edges.

1477 is a value of n for which n! + 1 is prime.

1479 is the number of planar partitions of 12.

1481 is a number n for which n, n+2, n+6, and n+8 are all prime.

1485 is the number of 3-colored rooted trees with 5 vertices.

1490 is the 14th tetranacci number.

1494 is the sum of its proper divisors that contain the digit 4.

1496 is the sum of the first 16 squares.

1497 is a Perrin number.

1500 = (5+1)(5+5)(5+0)(5+0).

1503 is a Friedman number.

1505 is a value of n for which σ(n-1) = σ(n+1).

1506 is the sum of its proper divisors that contain the digit 5.

1508 is a heptagonal pyramidal number.

1514 is a number whose square and cube use different digits.

1515 is the number of trees on 15 vertices with diameter 6.

1517 is the product of two consecutive primes.

1518 is the sum of its proper divisors that contain the digit 5.

1521 is the smallest number that can be written as the sum of 4 distinct

cubes in 3 ways.

1530 is a vampire number.

1531 appears inside its 4th power.

1533 is a Kaprekar constant in base 2.

1534 = 4321 in base 7.

1536 is not the sum of 4 non-zero squares.

1537 has its largest proper divisor as a substring.

1540 is a tetrahedal triangular number.

1541 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

1543 = 1111 + 55 + 44 + 333.

1547 is a hexagonal pyramidal number.

1549 is the smallest mutli-digit number that is not the sum of a prime and a

non-trivial power.

1555 is the largest n so that Q(√n) has class number 4.

1557 has a square where the first 6 digits alternate.

1560 is the maximum number of pieces a torus can be cut into with 20 cuts.

1562 = 22222 in base 5.

1563 is the smallest number with the property that its first 4 multiples

contain the digit 6.

1568 is the smallest Rhonda number.

1573 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

1575 is the number of partitions of 24.

1578 is the number of Hamiltonian paths of a 3×8 rectangle graph.

1581 is the smallest number whose 8th power contains exactly the same digits

as another 8th power.

1582 is a value of n so that n(n+4) is a palindrome.

1584 has a base 3 representation that ends with its base 6 representation.

1585 has a base 3 representation that ends with its base 6 representation.

1586 has a base 3 representation that ends with its base 6 representation.

1595 is the smallest quasi-Carmichael number in base 2.

1597 is the 17th Fibonacci number.

1600 = 4444 in base 7.

1601 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

1605 is the number of 7-octs.

1606 is the number of strongly connected digraphs with 4 vertices.

1609 is the largest known number n so that 38n - 37n is prime.

1610 is the number of partitions of 43 into distinct parts.

1613 is the largest known number n so that 82n - 81n is prime.

1624 is the Stirling number of the first kind s(7,3).

1629 is an icosahedral number.

1632 is the smallest number with the property that its first 5 multiples

contain the digit 6.

1633 is a number whose square and cube use different digits.

1634 = 14 + 64 + 34 + 44.

1635 has a fifth root whose decimal part starts with the digits 1-9 in some

order.

1636 appears inside its 4th power.

1638 is a harmonic divisor number.

1639 is the number of binary rooted trees with 16 vertices.

1640 = 2222 in base 9.

1648 is a betrothed number.

1649 is a Leyland number.

1650 is the number of connected partial orders on 7 unlabeled elements.

1657 is a Cuban prime.

1663 is the number of partitions of 41 in which no part occurs only once.

1664 is a value of n so that n(n+9) is a palindrome.

1665 is the number of triangles of any size contained in the triangle of

side 18 on a triangular grid.

1666 is the sum of the Roman numerals.

1668 is the maximum number of regions space can be divided into by 18

spheres.

1673 is a number whose sum of squares of the divisors is a square.

1676 = 11 + 62 + 73 + 64.

1680 is the smallest number with 40 divisors.

1681 is a square and each of its two 2-digit parts is square.

1683 is a Delannoy number.

1684 is the number of multigraphs with 6 vertices and 9 edges.

1688 is a truncated tetrahedral number.

1689 is the smallest composite number all of whose divisors (except 1)

contain the digit 9.

1691 is the number of multigraphs with 5 vertices and 11 edges.

1692 has a square with the first 3 digits the same as the next 3 digits.

1693 is the largest known number n so that 16n - 15n is prime.

1694 has a cube whose digits occur with the same frequency.

1695 is a rhombic dodecahedral number.

1696 is the number of regions formed when all diagonals are drawn in a

regular 16-gon.

1699 is the largest known number n so that 75n - 74n is prime.

1701 is the Stirling number of the second kind S(8,4).

1705 is the smallest quasi-Carmichael number in base 4.

1710 is the smallest non-palindrome where it and its reverse are divisible

by 19.

1711 is a triangular number that is the product of two primes.

1712 is the number of regions the complex plane is cut into by drawing lines

between all pairs of 16th roots of unity.

1713 is the number of 14-iamonds with holes.

1715 = (1) (7)3 (1) (5).

1716 = 13C6.

1722 is a Giuga number.

1728 = 123.

1729 is the smallest number which can be written as the sum of 2 cubes in 2

ways.

1730 is the sum of consecutive squares in 2 ways.

1734 is the sum of its proper divisors that contain the digit 8.

1738 = 6952 / 4, and this equation uses each digit 1-9 exactly once.

1739 has a base 5 representation that begins with its base 9 representation.

1740 has a base 5 representation that begins with its base 9 representation.

1755 = 3333 in base 8.

1763 is the product of twin primes.

1764 is the Stirling number of the first kind s(7,2).

1770 is the number of conjugacy classes in the automorphism group of the 13

dimensional hypercube.

1771 is a tetrahedral palindrome.

1782 is the smallest number n that is 3 times the sum of all the 2-digit

numbers that can be made using the digits of n.

1785 is a Kaprekar constant in base 2.

1787 is the number of different arrangements (up to rotation and reflection)

of 12 non-attacking queens on a 12×12 chessboard.

1789 is the smallest number with the property that its first 4 multiples

contain the digit 7.

1792 is a Friedman number.

1793 is a Pentanacci number.

1794 has a base 5 representation that begins with its base 9 representation.

1795 has a base 5 representation that begins with its base 9 representation.

1798 is a value of n for which φ(σ(n)) = φ(n).

1800 is a pentagonal pyramidal number.

1801 is a Cuban prime.

1804 is the number of 3×3 sliding puzzle positions that require exactly 14

moves to solve starting with the hole on a side.

1806 is a Schröder number.

1813 is the number of trees on 15 vertices with diameter 8.

1814 is the number of lattice points that are within 1/2 of a sphere of

radius 12 centered at the origin.

1816 is the number of partitions of 44 into distinct parts.

1818 evenly divides the sum of its rotations.

1820 = 16C4.

1822 has a cube that contains only even digits.

1823 has a square with the first 3 digits the same as the next 3 digits.

1824 has a cube that contains only even digits.

1827 is a vampire number.

1828 is the 6th meandric number and the 11th open meandric number.

1830 is the number of ternary square-free words of length 19.

1834 is an octahedral number.

1835 is the number of Pyramorphix puzzle positions that require exactly 4

moves to solve.

1837 is a value of n for which 2n and 7n together use the digits 1-9 exactly

once.

1842 is the number of rooted trees with 11 vertices.

1847 is the number of 2×2×2 Rubik cube positions that require exactly 4

moves to solve.

1848 is the number of quaternary square-free words of length 7.

1849 is the smallest composite number all of whose divisors (except 1)

contain the digit 4.

1854 is the number of derangements of 7 items.

1858 is the number of isomers of C14H30.

1860 is the number of ways to 12-color the faces of a tetrahedron.

1862 is the number of chess positions that can be reached in only one way

after 2 moves by white and 1 move by black.

1865 = 12345 in base 6.

1870 is the product of two consecutive Fibonacci numbers.

1871 is a number n for which n, n+2, n+6, and n+8 are all prime.

1873 is a value of n for which one less than the product of the first n

primes is prime.

1875 is the smallest order for which there are 21 groups.

1880 is a number whose sum of squares of the divisors is a square.

1885 is a Zeisel number.

1890 is the smallest number whose divisors contain every digit at least four

times.

1891 is a triangular number that is the product of two primes.

1893 is the number of 3×3 sliding puzzle positions that require exactly 14

moves to solve starting with the hole in a corner.

1895 is a value of n for which n, 2n, 3n, 4n, 5n, and 6n all use the same

number of digits in Roman numerals.

1897 is a Padovan number.

1900 is the largest palindrome in Roman numerals.

1902 has a cube that contains only even digits.

1905 is a Kaprekar constant in base 2.

1908 is the number of self-dual planar graphs with 22 edges.

1911 is a heptagonal pyramidal number.

1913 is prime and contains the same digits as the next prime.

1915 is the number of semigroups of order 5.

1917 is the number of possible configurations of pegs (up to symmetry) after

27 jumps in solitaire.

1920 is the smallest number that contains more different digits than its

cube.

1925 is a hexagonal pyramidal number.

1933 is a prime factor of 111111111111111111111.

1936 is a hexanacci number.

1944 is a member of the Fibonacci-like multiplication series starting with 2

and 3.

1945 is the number of triangles of any size contained in the triangle of

side 19 on a triangular grid.

1947 is the number of planar partitions of 16.

1950 = 144 + 145 + . . . + 156 = 157 + 158 + . . . + 168.

1951 is a Cuban prime.

1953 is a Kaprekar constant in base 2.

1957 is the number of permutations of some subset of 6 elements.

1958 is the number of partitions of 25.

1960 is the Stirling number of the first kind s(8,5).

1962 is a value of n for which 2n and 9n together use the digits 1-9 exactly

once.

1963 7852 / 4, and this equation uses each digit 1-9 exactly once.

1964 is the number of legal knight moves in chess.

1969 is the only known counterexample to a conjecture about modular

Ackermann functions.

1976 is the maximum number of regions space can be divided into by 19

spheres.

1979 has a sixth root whose decimal part starts with the digits 1-9 in some

order.

1980 is the number of ways to fold a 2×4 rectangle of stamps.

1983 is a Perrin number.

1990 is a stella octangula number.

1997 is a prime factor of 87654321.

1998 is the largest number that is the sum of its digits and the cube of its

digits.

2000 = 5555 in base 7.

2001 has a square with the first 3 digits the same as the next 3 digits.

2002 = 14C5.

2004 has a square with the last 3 digits the same as the 3 digits before

that.

2008 is a Kaprekar constant in base 3.

2010 is the number of trees on 15 vertices with diameter 7.

2015 is the number of trees on 18 vertices with diameter 5.

2016 is a value of n for which n2 + n3 contains one of each digit.

2017 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

2020 is a curious number.

2021 is the product of two consecutive primes.

2024 = 24C3.

2025 is a square that remains square if all its digits are incremented.

2027 is the largest known number n so that 7n - 6n is prime.

2030 is the smallest number that can be written as a sum of 3 or 4

consecutive squares.

2034 is the number of self-avoiding walks of length 9.

2038 is the number of Eulerian graphs with 9 vertices.

2041 is a 12-hyperperfect number.

2045 is the number of unlabeled partially ordered sets of 7 elements.

2046 is the maximum number of pieces a torus can be cut into with 22 cuts.

2047 is the smallest composite Mersenne number with prime exponent.

2048 is the smallest 11th power (besides 1).

2049 is a Cullen number.

2053 is a value of n for which one less than the product of the first n

primes is prime.

2061 is the number of sets of distinct positive integers with mean 7.

2067 is a value of n so that n(n+5) is a palindrome.

2073 is a Genocchi number.

2078 has a cube whose digits occur with the same frequency.

2080 is the number of different arrangements (up to rotation and reflection)

of 26 non-attacking bishops on a 14×14 chessboard.

2081 is a number n for which n, n+2, n+6, and n+8 are all prime.

2082 is the sum of its proper divisors that contain the digit 4.

2100 is divisible by its reverse.

2109 is a value of n so that n(n+7) is a palindrome.

2110 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

2112 has a fifth root whose decimal part starts with the digits 1-9 in some

order.

2114 is a number whose product of digits is equal to its sum of digits.

2116 has a base 10 representation which is the reverse of its base 7

representation.

2126 is a value of n so that n(n+3) is a palindrome.

2132 is the maximum number of 11th powers needed to sum to any number.

2133 is a 2-hyperperfect number.

2141 is a number whose product of digits is equal to its sum of digits.

2143 is the number of commutative semigroups of order 6.

2146 is a value of n for which 2φ(n) = φ(n+1).

2147 has a square with the last 3 digits the same as the 3 digits before

that.

2150 divides the sum of the largest prime factors of the first 2150 positive

integers.

2161 is a prime factor of 111111111111111111111111111111.

2164 is the smallest number whose 7th power starts with 5 identical digits.

2169 is a Leyland number.

2176 is the number of prime knots with 12 crossings.

2178 is the only number known which when multiplied by its reverse yields a

4th power.

2182 is the number of degree 15 irreducible polynomials over GF(2).

2184 is the product of three consecutive Fibonacci numbers.

2185 is the number of digits of 555.

2186 = 2222222 in base 3.

2187 is a strong Friedman number.

2188 is the 10th Motzkin number.

2194 is the number of partitions of 42 in which no part occurs only once.

2197 = 133.

2201 is the only non-palindrome known to have a palindromic cube.

2202 is a factor of the sum of the digits of 22022202.

2203 is the exponent of a Mersenne prime.

2207 is the 16th Lucas number.

2208 is a Keith number.

2210 = 47C2 + 47C2 + 47C1 + 47C0.

2213 = 23 + 23 + 133.

2217 has a base 2 representation that begins with its base 3 representation.

2219 is the number of 14-hexes with reflectional symmetry.

2222 is the smallest number divisible by a 1-digit prime, a 2-digit prime,

and a 3-digit prime.

2223 is a Kaprekar number.

2226 is the number of ways to 6-color the faces of a cube.

2235 is a value of n so that n(n+8) is a palindrome.

2244 is a number whose square and cube use different digits.

2252 is a Franel number.

2255 is the number of triangles of any size contained in the triangle of

side 20 on a triangular grid.

2257 = 4321 in base 8.

2260 is an icosahedral number.

2261 = 2222 + 22 + 6 + 11.

2263 = 2222 + 2 + 6 + 33.

2269 is a Cuban prime.

2272 is the number of graphs on 7 vertices with no isolated vertices.

2273 is the number of functional graphs on 10 vertices.

2274 is the sum of its proper divisors that contain the digit 7.

2275 is the sum of the first 6 4th powers.

2281 is the exponent of a Mersenne prime.

2285 is a non-palindrome with a palindromic square.

2295 is the number of self-dual binary codes of length 12.

2300 = 25C3.

2303 is a number whose square and cube use different digits.

2304 is the number of edges in a 9 dimensional hypercube.

2305 has a base 6 representation that ends with its base 8 representation.

2306 has a base 6 representation that ends with its base 8 representation.

2307 has a base 6 representation that ends with its base 8 representation.

2308 has a base 6 representation that ends with its base 8 representation.

2309 has a base 6 representation that ends with its base 8 representation.

2310 is the product of the first 5 primes.

2311 is a Euclid number.

2312 has a square with the first 3 digits the same as the next 3 digits.

2318 is the number of connected planar graphs with 10 edges.

2320 is the maximum number of regions space can be divided into by 20

spheres.

2322 is the number of connected graphs with 10 edges.

2323 is the maximum number of pieces a torus can be cut into with 23 cuts.

2325 is the maximum number of regions a cube can be cut into with 24 cuts.

2328 is the number of groups of order 128.

2331 is a centered cube number.

2336 is the number of sided 11-iamonds.

2339 is the number of ways to tile a 6×10 rectangle with the pentominoes.

2340 = 4444 in base 8.

2343 = 33333 in base 5.

2345 has digits in arithmetic sequence.

2349 is a Friedman number.

2354 = 2222 + 33 + 55 + 44.

2357 is the concatenation of the first 4 primes.

2359 = 2222 + 33 + 5 + 99.

2360 is a hexagonal pyramidal number.

2368 is the number of 3×3 sliding puzzle positions that require exactly 14

moves to solve starting with the hole in the center.

2371 is the largest known number n so that 100n - 99n is prime.

2377 is a value of n for which one less than the product of the first n

primes is prime.

2378 is the 10th Pell number.

2380 = 17C4.

2385 is the smallest number whose 7th power contains exactly the same digits

as another 7th power.

2388 is the number of 3-connected graphs with 8 vertices.

2394 is a value of n for which n and 7n together use each digit 1-9 exactly

once.

2398 is the number of 3×3 sliding puzzle positions that require exactly 28

moves to solve starting with the hole in the center.

2399 is the largest known number n so that 67n - 66n is prime.

2400 = 6666 in base 7.

2401 is the 4th power of the sum of its digits.

2402 has a base 2 representation that begins with its base 7 representation.

2411 is a number whose product of digits is equal to its sum of digits.

2414 is the number of symmetric plane partitions of 28.

2417 has a base 3 representation that begins with its base 7 representation.

2420 is the number of possible rook moves on a 11×11 chessboard.

2427 = 21 + 42 + 23 + 74.

2431 is the product of 3 consecutive primes.

2434 is the number of legal king moves in chess.

2436 is the number of partitions of 26.

2437 is the smallest number which is not prime when preceded or followed by

any digit 1-9.

2445 is a truncated tetrahedral number.

2448 is the order of a non-cyclic simple group.

2450 has a base 3 representation that begins with its base 7 representation.

2457 = 169 + 170 + . . . + 182 = 183 + 184 + . . . + 195.

2460 = 3333 in base 9.

2465 is a Carmichael number.

2466 is the number of regions formed when all diagonals are drawn in a

regular 188-gon.

2467 has a square with the first 3 digits the same as the next 3 digits.

2468 has digits in arithmetic sequence.

2469 is a value of n for which 4n and 5n together use the digits 1-9 exactly

once.

2470 is the sum of the first 19 squares.

2473 is the largest known number n so that 40n - 39n is prime.

2477 is the largest known number n so that 50n - 49n is prime.

2484 is the number of regions the complex plane is cut into by drawing lines

between all pairs of 18th roots of unity.

2485 is the number of planar partitions of 13.

2491 is the product of two consecutive primes.

2498 is the number of lattice points that are within 1/2 of a sphere of

radius 14 centered at the origin.

2499 is the number of connected planar Eulerian graphs with 10 vertices.

2500 is a tetranacci number.

2501 is a Friedman number.

2502 is a strong Friedman number.

2503 is a Friedman number.

2504 is a Friedman number.

2505 is a Friedman number.

2506 is a Friedman number.

2507 is a Friedman number.

2508 is a Friedman number.

2509 is a Friedman number.

2511 is the smallest number so that it and its successor are both the

product of a prime and the 4th power of a prime.

2512 is the number of 3×3 sliding puzzle positions that require exactly 15

moves to solve starting with the hole in a corner.

2513 is a Padovan number.

2515 is the number of symmetric 9-cubes.

2517 is the number of regions the complex plane is cut into by drawing lines

between all pairs of 17th roots of unity.

2518 uses the same digits as φ(2518).

2519 is the smallest number n where either n or n+1 is divisible by the

numbers from 1 to 12.

2520 is the smallest number divisible by 1 through 10.

2524 and the two numbers before it and after it are all products of exactly

3 primes.

2525 and the two numbers before it and after it are all products of exactly

3 primes.

2530 is a Leyland number.

2531 is the largest known number n so that 10n - 9n is prime.

2532 = 2222 + 55 + 33 + 222.

2535 is the number of ways to 13-color the faces of a tetrahedron.

2538 has a square with 5/7 of the digits are the same.

2542 is the number of stretched 9-ominoes.

2549 is the largest known number n so that 54n - 53n is prime.

2550 is a Kaprekar constant in base 4.

2557 is the largest known number n so that 35n - 34n is prime.

2571 is the smallest number with the property that its first 7 multiples

contain the digit 1.

2576 has exactly the same digits in 3 different bases.

2580 is a Keith number.

2584 is the 18th Fibonacci number .

2590 is the number of partitions of 47 into distinct parts.

2592 = 25 92.

2593 has a base 3 representation that ends with its base 6 representation.

2594 has a base 3 representation that ends with its base 6 representation.

2596 is the number of triangles of any size contained in the triangle of

side 21 on a triangular grid.

2600 = 26C3.

2601 is a pentagonal pyramidal number.

2606 is the number of polyhedra with 9 vertices.

2609 is the number of perfect squared rectangles of order 15.

2615 is the number of functions from 9 unlabeled points to themselves.

2620 is an amicable number.

2621 = 2222 + 66 + 222 + 111.

2622 is a value of n for which 7n and 8n together use each digit exactly

once.

2623 = 2222 + 66 + 2 + 333.

2624 is the maximum number of pieces a torus can be cut into with 24 cuts.

2626 is the maximum number of regions a cube can be cut into with 25 cuts.

2627 is a Perrin number.

2629 is the smallest number whose reciprocal has period 14.

2636 is a non-palindrome with a palindromic square.

2637 is a value of n for which n and 7n together use each digit 1-9 exactly

once.

2646 is the Stirling number of the second kind S(9,6).

2651 is a stella octangula number.

2657 is a value of n for which one more than the product of the first n

primes is prime.

2662 is a palindrome and the 2662nd triangular number is a palindrome.

2665 is the number of conjugacy classes in the automorphism group of the 14

dimensional hypercube.

2667 is a number whose sum of divisors is a 4th power.

2671 is a value of n for which 2n and 7n together use the digits 1-9 exactly

once.

2672 and its successor are both divisible by 4th powers.

2673 is the smallest number that can be written as the sum of 3 4th powers

in 2 ways.

2680 is the number of different arrangements of 11 non-attacking queens on

an 11×11 chessboard.

2683 is the largest n so that Q(√n) has class number 5.

2685 is a value of n for which σ(n) = σ(n+1).

2694 is the number of ways 22 people around a round table can shake hands in

a non-crossing way, up to rotation.

2697 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

2700 is the product of the first 5 triangular numbers.

2701 is the smallest number n which divides the average of the nth prime and

the primes surrounding it.

2702 is the maximum number of regions space can be divided into by 21

spheres.

2704 is the number of necklaces with 9 white and 9 black beads.

2710 is an hexagonal prism number.

2725 is the number of fixed octominoes.

2728 is a Kaprekar number.

2729 has a square with the first 3 digits the same as the next 3 digits.

2730 = 15P3.

2731 is a Wagstaff prime.

2736 is an octahedral number.

2737 is a strong Friedman number.

2741 is the largest known number n so that 94n - 93n is prime.

2744 = 143.

2745 divides the sum of the primes less than it.

2749 is the smallest index of a Fibonacci number whose first 9 digits are

the digits 1-9 rearranged.

2753 is the number of subsequences of {1,2,3,...13} in which every odd

number has an even neighbor.

2757 is the number of possible configurations of pegs (up to symmetry) after

7 jumps in solitaire.

2758 has the property that placing the last digit first gives 1 more than

triple it.

2766 in hexadecimal spells the word ACE.

2769 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

2780 = 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81.

2786 is the 9th Pell-Lucas number.

2791 is a Cuban prime.

2801 = 11111 in base 7.

2802 is the sum of its proper divisors that contain the digit 4.

2805 is the smallest order of a cyclotomic polynomial whose factorization

contains 6 as a coefficient.

2812 is the number of 8-pents.

2817 uses the same digits as φ(2817).

2821 is a Carmichael number.

2828 is a value of n so that n(n+8) is a palindrome.

2835 is a Rhonda number.

2837 is the largest known number n so that 17n - 16n is prime.

2842 is the smallest number with the property that its first 4 multiples

contain the digit 8.

2856 = 17!!!!!.

2857 is the number of partitions of 44 in which no part occurs only once.

2858 has a square with the first 3 digits the same as the next 3 digits.

2863 has a tenth root whose decimal part starts with the digits 1-9 in some

order.

2868 has a 4th power containing only 4 different digits.

2870 is the sum of the first 20 squares.

2872 is the 15th tetranacci number.

2874 is the number of multigraphs with 5 vertices and 12 edges.

2876 is the number of 8-hepts.

2880 is the smallest number that can be written in the form (a2-1)(b2-1) in

3 ways.

2881 has a base 3 representation that ends with its base 6 representation.

2882 has a base 3 representation that ends with its base 6 representation.

2890 is the smallest number in base 9 whose square contains the same digits

in the same proportion.

2893 is the number of planar 2-connected graphs with 8 vertices.

2900 is the number of self-avoiding walks in a quadrant of length 10.

2910 is the number of partitions of 48 into distinct parts.

2911 is a value of n for which σ(n-1) = σ(n+1).

2914 is a value of n for which σ(n-1) = σ(n+1).

2916 is a Friedman number.

2920 is a heptagonal pyramidal number.

2922 is the sum of its proper divisors that contain the digit 4.

2924 is an amicable number.

2925 = 27C3.

2928 is the number of partitions of 45 in which no part occurs only once.

2931 is the number of trees on 16 vertices with diameter 6.

2937 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

2938 is the number of binary rooted trees with 17 vertices.

2947 is the smallest number whose 5th power starts with 4 identical digits.

2950 is the maximum number of pieces a torus can be cut into with 25 cuts.

2952 is the maximum number of regions a cube can be cut into with 26 cuts.

2955 has a 5th power whose digits all occur twice.

2967 is a value of n for which 5n and 7n together use each digit exactly

once.

2968 is the number of ways to place 2 non-attacking kings on a 9×9

chessboard.

2970 is a harmonic divisor number.

2971 is the index of a prime Fibonacci number.

2973 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

2974 is a value of n for which σ(n) = σ(n+1).

2981 is the closest integer to e8.

2982 is a value of n so that n(n+7) is a palindrome.

2991 uses the same digits as φ(2991).

2996 = 2222 + 99 + 9 + 666.

2997 = 222 + 999 + 999 + 777.

2998 is a value of n so that n(n+3) is a palindrome.

2999 = 2 + 999 + 999 + 999.

3003 is the only number known to appear 8 times in Pascal's triangle.

3006 has a square with the last 3 digits the same as the 3 digits before

that.

3008 is the number of symmetric plane partitions of 29.

3010 is the number of partitions of 27.

3012 is the sum of its proper divisors that contain the digit 5.

3015 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

3020 is the closest integer to π7.

3024 = 9P4.

3025 is the sum of the first 10 cubes.

3031 is the number of 7-kings.

3032 is the number of trees on 19 vertices with diameter 5.

3036 is the sum of its proper divisors that contain the digit 5.

3045 = 196 + 197 + . . . + 210 = 211 + 212 + . . . + 224.

3058 is the number of 7-digit triangular numbers.

3059 is a centered cube number.

3060 = 18C4.

3068 is the number of 10-ominoes that tile the plane.

3069 is a Kaprekar constant in base 2.

3070 is the number of paraffins with 9 carbon atoms.

3078 is a pentagonal pyramidal number.

3084 is the number of 3×3 sliding puzzle positions that require exactly 15

moves to solve starting with the hole in the center.

3094 = 21658 / 7, and each digit from 0-9 is contained in the equation

exactly once.

3096 is the number of 3×3×3 sliding puzzle positions that require exactly 7

moves to solve.

3097 is the largest known number n with the property that in every base,

there exists a number that is n times the sum of its digits.

3103 = 22C3 + 22C1 + 22C0 + 22C3.

3106 is both the sum of the digits of the 16th and the 17th Mersenne prime.

3109 is the largest known number n so that 91n - 90n is prime.

3110 = 22222 in base 6.

3114 has a square containing only 2 digits.

3120 is the product of the first 6 Fibonacci numbers.

3124 = 44444 in base 5.

3125 is a strong Friedman number.

3126 is a Sierpinski Number of the First Kind.

3127 is the product of two consecutive primes.

3135 is the smallest order of a cyclotomic polynomial whose factorization

contains 7 as a coefficient.

3136 is a square that remains square if all its digits are decremented.

3137 is the number of planar partitions of 17.

3148 has a square with the first 3 digits the same as the next 3 digits.

3150 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

3156 is the sum of its proper divisors that contain the digit 5.

3159 is the number of trees with 14 vertices.

3160 is the largest known n for which 2n!/(n!)2 does not contain a prime

factor less than 12.

3168 has a square whose reverse is also a square.

3169 is a Cuban prime.

3174 is the sum of its proper divisors that contain the digit 5.

3178 = 4321 in base 9.

3180 has a base 3 representation that ends with its base 5 representation.

3181 has a base 3 representation that ends with its base 5 representation.

3182 has a base 3 representation that ends with its base 5 representation.

3186 is a value of n for which 5n and 9n together use each digit exactly

once.

3187 and its product with 8 contain every digit from 1-9 exactly once.

3190 is the number of Hamiltonian paths of a 3×9 rectangle graph.

3191 is the smallest number whose reciprocal has period 29.

3200 is the number of graceful permutations of length 13.

3210 is the smallest 4-digit number with decreasing digits.

3212 = 37 + 29 + 17 + 29.

3216 is the smallest number with the property that its first 6 multiples

contain the digit 6.

3217 is the exponent of a Mersenne prime.

3225 is the number of symmetric 3×3 matrices in base 5 with determinant 0.

3229 is a value of n for which one more than the product of the first n

primes is prime.

3240 is the number of 3×3×3 Rubik cube positions that require exactly 3

moves to solve.

3242 has a square with the first 3 digits the same as the next 3 digits.

3248 is the number of legal bishop moves in chess.

3249 is the smallest square that is comprised of two squares that overlap in

one digit.

3251 is a number n for which n, n+2, n+6, and n+8 are all prime.

3254 = 33 + 2222 + 555 + 444.

3259 = 33 + 2222 + 5 + 999.

3264 is the number of partitions of 49 into distinct parts.

3267 = 12345 in base 7.

3276 = 28C3.

3280 = 11111111 in base 3.

3281 is the sum of consecutive squares in 2 ways.

3282 is the sum of its proper divisors that contain the digit 4.

3283 is the number of 3×3 sliding puzzle positions that require exactly 15

moves to solve starting with the hole on a side.

3294 is a value of n for which 6n and 7n together use each digit exactly

once.

3297 is a value of n for which 5n and 7n together use each digit exactly

once.

3300 is the number of non-isomorphic groupoids on 4 elements.

3301 is a value of n for which the nth Fibonacci number begins with the

digits in n.

3302 is the maximum number of pieces a torus can be cut into with 26 cuts.

3304 is the maximum number of regions a cube can be cut into with 27 cuts.

3305 is a value of n for which σ(n-1) = σ(n+1).

3311 is the sum of the first 21 squares.

3313 is the smallest prime number where every digit d occurs d times.

3318 has exactly the same digits in 3 different bases.

3320 has a base 4 representation that ends with 3320.

3321 has a base 4 representation that ends with 3321.

3322 has a base 4 representation that ends with 3322.

3323 has a base 4 representation that ends with 3323.

3329 is a Padovan number.

3331 is the largest known number n so that 53n - 52n is prime.

3333 is a repdigit.

3334 is the number of 12-iamonds.

3338 is the number of lattice points that are within 1/2 of a sphere of

radius 16 centered at the origin.

3340 = 3333 + 3 + 4 + 0.

3341 = 3333 + 3 + 4 + 1.

3342 = 3333 + 3 + 4 + 2.

3343 = 3333 + 3 + 4 + 3.

3344 = 3333 + 3 + 4 + 4.

3345 = 3333 + 3 + 4 + 5.

3346 = 3333 + 3 + 4 + 6.

3347 = 3333 + 3 + 4 + 7.

3348 = 3333 + 3 + 4 + 8.

3349 = 3333 + 3 + 4 + 9.

3360 = 16P3.

3367 is the smallest number which can be written as the difference of 2

cubes in 3 ways.

3368 is the number of ways that 8 non-attacking bishops can be placed on a

5×5 chessboard.

3369 is a Kaprekar constant in base 4.

3375 is a Friedman number.

3378 is a Friedman number.

3379 is a number whose square and cube use different digits.

3381 is the number of ways to 14-color the faces of a tetrahedron.

3382 is a value of n for which 2φ(n) = φ(n+1).

3400 is a truncated tetrahedral number.

3402 can be written as the sum of 2, 3, 4, or 5 cubes.

3403 is a triangular number that is the product of two primes.

3413 = 11 + 22 + 33 + 44 + 55.

3417 is a hexagonal pyramidal number.

3420 is the order of a non-cyclic simple group.

3432 is the 7th central binomial coefficient.

3435 = 33 + 44 + 33 + 55.

3439 is a rhombic dodecahedral number.

3444 is a stella octangula number.

3447 is a value of n for which 2n and 5n together use the digits 1-9 exactly

once.

3456 has digits in arithmetic sequence.

3461 is a number n for which n, n+2, n+6, and n+8 are all prime.

3465 = 15!!!!.

3468 = 682 - 342.

3476 is a value of n for which n!! - 1 is prime.

3480 is a Perrin number.

3486 has a square that is formed by 3 squares that overlap by 1 digit.

3489 is the smallest number whose square has the first 3 digits the same as

the last 3 digits.

3492 is the number of labeled semigroups of order 4.

3501 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

3510 = 6666 in base 8.

3511 is the largest known Wieferich prime.

3521 = 3333 + 55 + 22 + 111.

3522 is the sum of its proper divisors that contain the digit 7.

3525 is a Pentanacci number.

3527 is the number of ways to fold a strip of 10 stamps.

3531 is a value of n for which φ(n) = φ(n-2) - φ(n-1).

3536 is a heptagonal pyramidal number.

3541 is the smallest number whose reciprocal has period 20.

3543 has a cube containing only 3 different digits.

3571 is the 17th Lucas number.

3577 is a Kaprekar constant in base 2.

3579 has digits in arithmetic sequence.

3584 is not the sum of 4 non-zero squares.

3588 is the maximum number of regions space can be divided into by 23

spheres.

3599 is the product of twin primes.

3600 is a value of n for which n, 2n, 3n, 4n, 5n, 6n, and 7n all use the

same number of digits in Roman numerals.

3607 is a prime factor of 123456789.

3610 is a pentagonal pyramidal number.

3624 is the smallest number n where n through n+3 are all products of 4 or

more primes.

3630 appears inside its 4th power.

3635 has a square with the first 3 digits the same as the next 3 digits.

3640 = 13!!!.

3641 is an hexagonal prism number.

3645 is the maximum determinant of a 12×12 matrix of 0's and 1's.

3654 = 29C3.

3655 is the sum of consecutive squares in 2 ways.

3658 is the number of partitions of 50 into distinct parts.

3671 is the number of 9-abolos.

3678 has a square comprised of the digits 1-8.

3681 is the maximum number of pieces a torus can be cut into with 27 cuts.

3683 is the maximum number of regions a cube can be cut into with 28 cuts.

3684 is a Keith number.

3685 is a strong Friedman number.

3697 is the smallest number in base 6 whose square contains the same digits

in the same proportion.

3698 has a square comprised of the digits 0-7.

3709 is a value of n for which 2n and 7n together use the digits 1-9 exactly

once.

3711 is the number of multigraphs with 6 vertices and 10 edges.

3718 is the number of partitions of 28.

3720 = 225 + 226 + . . . + 240 = 241 + 242 + . . . + 255.

3721 is the number of partitions of 46 in which no part occurs only once.

3722 is the number of lattice points that are within 1/2 of a sphere of

radius 17 centered at the origin.

3729 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

3740 is the sum of consecutive squares in 2 ways.

3743 is the number of polyaboloes with 9 half squares.

3745 has a square with the last 3 digits the same as the 3 digits before

that.

3747 is the smallest number whose 9th power contains exactly the same digits

as another 9th power.

3763 is the largest n so that Q(√n) has class number 6.

3771 is a value of n for which 4n and 7n together use each digit exactly

once.

3784 has a factorization using the same digits as itself.

3786 = 34 + 74 + 8 + 64.

3791 is the number of symmetric plane partitions of 30.

3792 occurs in the middle of its square.

3795 is the sum of the first 22 squares.

3797 is the largest known number n so that 14n - 13n is prime.

3798 is a value of n for which 2n and 9n together use the digits 1-9 exactly

once.

3803 is the largest prime factor of 123456789.

3807 and its successor are both divisible by 4th powers.

3810 is the number of ways to place a non-attacking white and black pawn on

a 9×9 chessboard.

3813 is the number of partitions of 47 in which no part occurs only once.

3822 is the number of triangles of any size contained in the triangle of

side 24 on a triangular grid.

3825 is a Kaprekar constant in base 2.

3832 is the number of fixed 6-kings.

3836 is the maximum number of inversions in a permutation of length 7.

3840 = 10!!

3843 is a value of n for which 7n and 9n together use each digit exactly

once.

3846 is the number of Hamiltonian cycles of a 4×11 rectangle graph.

3849 has a square with the first 3 digits the same as the next 3 digits.

3861 is the smallest number whose 4th power starts with 5 identical digits.

3864 is a strong Friedman number.

3873 is a Kaprekar constant in base 4.

3876 = 19C4.

3882 is the sum of its proper divisors that contain the digit 4.

3894 is an octahedral number.

3900 has a base 2 representation that is two copies of its base 5

representation concatenated.

3901 has a base 2 representation that ends with its base 5 representation.

3906 = 111111 in base 5.

3907 = 15628 / 4, and each digit from 0-9 is contained in the equation

exactly once.

3910 is the number of 3×3 sliding puzzle positions that require exactly 28

moves to solve starting with the hole in a corner.

3911 and its reverse are prime, even if we append or prepend a 3 or 9.

3912 is a value of n for which 5n and 7n together use each digit exactly

once.

3919 is the largest known number n so that 37n - 36n is prime.

3920 = (5+3)(5+9)(5+2)(5+0).

3925 is a centered cube number.

3926 is the 12th open meandric number.

3927 has an eighth root whose decimal part starts with the digits 1-9 in

some order.

3937 is a Kaprekar constant in base 2.

3942 is a value of n for which n and 4n together use each digit 1-9 exactly

once.

3956 is the number of conjugacy classes in the automorphism group of the 15

dimensional hypercube.

3967 is the smallest number whose 12th power contains exactly the same

digits as another 12th power.

3968 and its successor are both divisible by 4th powers.

3969 is a Kaprekar constant in base 2.

3972 is a strong Friedman number.

3977 has its largest proper divisor as a substring.

3984 is a heptanacci number.

3985 = 3333 + 9 + 88 + 555.

4000 has a cube that contains only even digits.

4002 has a square with the first 3 digits the same as the next 3 digits.

4006 = 14C4 + 14C0 + 14C0 + 14C6.

4008 has a square with the last 3 digits the same as the 3 digits before

that.

4013 is a prime factor of 1111111111111111111111111111111111.

4029 is the number of regions formed when all diagonals are drawn in a

regular 19-gon.

4030 is an abundant number that is not the sum of some subset of its

divisors.

4032 is the number of connected bipartite graphs with 10 vertices.

4047 is a hexagonal pyramidal number.

4048 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

4051 is the number of partitions of 6 items into ordered lists.

4056 is the number of possible rook moves on a 13×13 chessboard.

4060 = 30C3.

4062 is the smallest number with the property that its first 8 multiples

contain the digit 2.

4080 = 17P3.

4087 is the product of two consecutive primes.

4088 is the maximum number of pieces a torus can be cut into with 28 cuts.

4090 is the maximum number of regions a cube can be cut into with 29 cuts.

4093 = 28651 / 7, and each digit from 0-9 is contained in the equation

exactly once.

4095 = 111111111111 in base 2.

4096 is the smallest number with 13 divisors.

4097 is the smallest number (besides 2) that can be written as the sum of

two cubes or the sum of two 4th powers.

4099 has a square with the last 3 digits the same as the 3 digits before

that.

4100 = 5555 in base 9.

4104 can be written as the sum of 2 cubes in 2 ways.

4106 is a Friedman number.

4112 is a number whose product of digits is equal to its sum of digits.

4121 is a number whose product of digits is equal to its sum of digits.

4128 is the smallest number with the property that its first 10 multiples

contain the digit 2.

4140 is the 8th Bell number.

4149 is a value of n for which σ(n-1) = σ(n+1).

4150 = 45 + 15 + 55 + 05.

4151 = 45 + 15 + 55 + 15.

4152 = 45 + 15 + 55 + 2.

4153 = 45 + 15 + 55 + 3.

4154 = 45 + 15 + 55 + 4.

4155 = 45 + 15 + 55 + 5.

4156 = 45 + 15 + 55 + 6.

4157 = 45 + 15 + 55 + 7.

4158 = 45 + 15 + 55 + 8.

4159 = 45 + 15 + 55 + 9.

4160 = 43 + 163 + 03.

4161 = 43 + 163 + 13.

4167 is a Friedman number.

4170 is the number of lattice points that are within 1/2 of a sphere of

radius 18 centered at the origin.

4175 has a square comprised of the digits 0-7.

4176 has an eighth root whose decimal part starts with the digits 1-9 in

some order.

4181 is the first composite number in the Fibonacci sequence with a prime

index.

4186 is a hexagonal, 13-gonal, triangular number.

4187 is the smallest Rabin-Miller pseudoprime with an odd reciprocal period.

4188 is a value of n for which σ(n-1) = σ(n+1).

4193 is the number of 3×3 sliding puzzle positions that require exactly 16

moves to solve starting with the hole on a side.

4199 is the product of 3 consecutive primes.

4200 is divisible by its reverse.

4204 and the two numbers before it and after it are all products of exactly

3 primes.

4207 is the number of cubic graphs with 16 vertices.

4211 is a number whose product of digits is equal to its sum of digits.

4216 is an octagonal pyramidal number.

4219 is a Cuban prime.

4223 is the maximum number of 12th powers needed to sum to any number.

4224 is a palindrome that is one less than a square.

4225 is the smallest number that can be written as the sum of two squares in

12 ways.

4231 is the number of labeled partially ordered sets with 5 elements.

4233 is a heptagonal pyramidal number.

4240 is a Leyland number.

4243 = 444 + 22 + 444 + 3333.

4146 is the number of ternary square-free words of length 22.

4253 is the exponent of a Mersenne prime.

4264 is a number whose sum of squares of the divisors is a square.

4279 is the smallest semiprime super-catalan number..

4293 has exactly the same digits in 3 different bases.

4297 is a value of n for which one less than the product of the first n

primes is prime.

4303 is the number of triangles of any size contained in the triangle of

side 25 on a triangular grid.

4305 has exactly the same digits in 3 different bases.

4310 has exactly the same digits in 3 different bases.

4312 is the smallest number whose 10th power starts with 7 identical digits.

4320 = (6+4)(6+3)(6+2)(6+0).

4321 has digits in arithmetic sequence.

4324 is the sum of the first 23 squares.

4332 = 444 + 3333 + 333 + 222.

4335 = 444 + 3333 + 3 + 555.

4336 = 4 + 3333 + 333 + 666.

4337 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

4339 = 4 + 3333 + 3 + 999.

4340 is the number of 3×3 sliding puzzle positions that require exactly 27

moves to solve starting with the hole in the center.

4342 appears inside its 4th power.

4343 divides the sum of the largest prime factors of the first 4343 positive

integers.

4347 is a value of n for which 2n and 5n together use the digits 1-9 exactly

once.

4349 is the largest known number n so that 46n - 45n is prime.

4352 has a cube that contains only even digits.

4356 is two thirds of its reverse.

4357 is the smallest number with the property that its first 5 multiples

contain the digit 7.

4358 is the number of lattice points that are within 1/2 of a sphere of

radius 19 centered at the origin.

4364 is a value of n for which σ(n) = sigma;(n+1).

4365 is a value of n for which 4n and 9n together use each digit exactly

once.

4368 = 16C5.

4374 and its successor are both divisible by 4th powers.

4381 is a stella octangula number.

4392 is a value of n for which n and 4n together use each digit 1-9 exactly

once.

4396 = (157)(28) and each digit is contained in the equation exactly once.

4409 is prime, but changing any digit makes it composite.

4410 is a Padovan number.

4418 is the number of 7-nons.

4423 is the exponent of a Mersenne prime.

4425 is the sum of the first 5 5th powers.

4434 is the sum of its proper divisors that contain the digit 7.

4435 uses the same digits as φ(4435).

4438 is the number of 15-hexes with reflectional symmetry.

4444 is a repdigit.

4445 is the smallest number that can be written as the sum of 4 distinct

positive cubes in 4 ways.

4447 is the largest known number n so that 66n - 65n is prime.

4463 is the largest known number n so that 12n - 11n is prime.

4480 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

4485 is the number of 3×3 sliding puzzle positions that require exactly 16

moves to solve starting with the hole in a corner.

4488 = 256 + 257 + . . . + 272 = 273 + 274 + . . . + 288.

4489 is a square whose digits are non-decreasing.

4495 = 31C3.

4498 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

4500 is the number of regions formed when all diagonals are drawn in a

regular 20-gon.

4503 is the largest number that is not the sum of 4 or fewer squares of

composites.

4505 is a Zeisel number.

4506 is the sum of its proper divisors that contain the digit 5.

4507 is the largest known number n so that 57n - 56n is prime.

4510 = 4444 + 55 + 11 + 0.

4511 = 4444 + 55 + 11 + 1.

4512 = 4444 + 55 + 11 + 2.

4513 = 4444 + 55 + 11 + 3.

4514 = 4444 + 55 + 11 + 4.

4515 = 4444 + 55 + 11 + 5.

4516 = 4444 + 55 + 11 + 6.

4517 = 4444 + 55 + 11 + 7.

4518 = 4444 + 55 + 11 + 8.

4519 = 4444 + 55 + 11 + 9.

4520 is the number of regions the complex plane is cut into by drawing lines

between all pairs of 20th roots of unity.

4523 has a square in base 2 that is palindromic.

4524 is the maximum number of pieces a torus can be cut into with 29 cuts.

4526 is the maximum number of regions a cube can be cut into with 30 cuts.

4527 is a value of n for which n and 7n together use each digit 1-9 exactly

once.

4535 is the number of unlabeled topologies with 7 elements.

4536 is the Stirling number of the first kind s(9,6).

4541 has a square with the first 3 digits the same as the next 3 digits.

4542 is the number of trees on 20 vertices with diameter 5.

4547 is a value of n for which one more than the product of the first n

primes is prime.

4548 is the sum of its proper divisors that contain the digit 7.

4550 is a value of n for which 2φ(n) = φ(n+1).

4552 has a square with the first 3 digits the same as the next 3 digits.

4565 is the number of partitions of 29.

4567 has digits in arithmetic sequence.

4576 is a truncated tetrahedral number.

4579 is an octahedral number.

4582 is the number of partitions of 52 into distinct parts.

4583 is a value of n for which one less than the product of the first n

primes is prime.

4589 is the index of a Fibonacci number whose first 9 digits are the digits

1-9 rearranged.

4607 is a Woodall number.

4608 is the number of ways to place 2 non-attacking kings on a 10×10

chessboard.

4609 is a Cullen number.

4610 is a Perrin number.

4613 is the number of graphs with 10 edges.

4616 has a square comprised of the digits 0-7.

4619 is a value of n for which 4n and 5n together use each digit exactly

once.

4620 is the largest order of a permutation of 30 or 31 elements.

4624 = 44 + 46 + 42 + 44.

4625 is the number of trees on 16 vertices with diameter 7.

4628 is a Friedman number.

4641 is a rhombic dodecahedral number.

4644 is a value of n for which 7n and 9n together use each digit exactly

once.

4649 is the largest prime factor of 1111111.

4650 is the maximum number of regions space can be divided into by 25

spheres.

4655 is the number of 10-ominoes.

4663 is the number of 12-ominoes that contain holes.

4665 = 33333 in base 6.

4676 is the sum of the first 7 4th powers.

4681 = 11111 in base 8.

4683 is the number of orderings of 6 objects with ties allowed.

4705 is the sum of consecutive squares in 2 ways.

4709 is the number of symmetric plane partitions of 31.

4713 is a value of n such that the nth Cullen number is prime.

4723 is the index of a prime Fibonacci number.

4730 is the number of multigraphs with 5 vertices and 13 edges.

4734 is the sum of its proper divisors that contain the digit 7.

4735 is a value of n for which 4n and 5n together use each digit exactly

once.

4741 is a value of n for which 4n and 5n together use each digit exactly

once.

4743 is a value of n for which 2n and 5n together use the digits 1-9 exactly

once.

4750 is a hexagonal pyramidal number.

4752 = (4+4)(4+7)(4+5)(4+2).

4755 has a cube whose digits occur with the same frequency.

4757 is the product of two consecutive primes.

4760 is the sum of consecutive squares in 2 ways.

4762 is the smallest number not a power of 10 whose square contains the same

digits.

4764 is an hexagonal prism number.

4766 is the number of rooted trees with 12 vertices.

4769 is a value of n for which 4n and 5n together use each digit exactly

once.

4787 is a value of n for which one more than the product of the first n

primes is prime.

4788 is a Keith number.

4793 = 4444 + 7 + 9 + 333.

4802 is the number of trees on 16 vertices with diameter 8.

4804 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

4807 is the smallest quasi-Carmichael number in base 10.

4819 is a tetranacci number.

4823 is the number of triangles of any size contained in the triangle of

side 26 on a triangular grid.

4832 is a number whose square contains the same digits.

4845 = 20C4.

4848 is the number of quaternary square-free words of length 8.

4851 is a pentagonal pyramidal number.

4862 is the 9th Catalan number.

4863 is the smallest number that cannot be written as the sum of 273 8th

powers.

4866 is the number of partitions of 48 in which no part occurs only once.

4869 is a value of n for which 3n and 8n together use each digit exactly

once.

4877 is the largest prime factor of 87654321.

4890 is the sum of the first 4 6th powers.

4893 is a value of n for which 2n and 7n together use the digits 1-9 exactly

once.

4895 is the product of two consecutive Fibonacci numbers.

4896 = 18P3.

4900 is the only number which is both square and square pyramidal (besides

1).

4901 has a base 3 representation that begins with its base 7 representation.

4913 is the cube of the sum of its digits.

4919 is the largest known number n so that 71n - 70n is prime.

4920 = 6666 in base 9.

4923 and the two numbers before it and after it are all products of exactly

3 primes.

4924 and the two numbers before it and after it are all products of exactly

3 primes.

4927 is a value of n for which 4n and 5n together use each digit exactly

once.

4931 is a value of n for which 2n and 7n together use the digits 1-9 exactly

once.

4941 is a centered cube number.

4960 = 32C3.

4967 is the number of partitions of 49 in which no part occurs only once.

4974 is the sum of its proper divisors that contain the digit 8.

4990 is the maximum number of pieces a torus can be cut into with 30 cuts.

4992 is the maximum number of regions a cube can be cut into with 31 cuts.

5000 is the largest number whose English name does not repeat any letters.

5001 appears inside its 4th power.

5002 has a 4th power containing only 4 different digits.

5005 is the smallest palindromic product of 4 consecutive primes.

5010 has a square with the last 3 digits the same as the 3 digits before

that.

5016 is a heptagonal pyramidal number.

5020 is an amicable number.

5034 is the number of lattice points that are within 1/2 of a sphere of

radius 20 centered at the origin.

5036 and the two numbers before it and after it are all products of exactly

3 primes.

5039 is the number of planar partitions of 18.

5040 = 7!

5041 is the largest square known of the form n! + 1.

5044 is a value of n for which φ(n) and σ(n) are square.

5049 is an octagonal pyramidal number.

5050 is the sum of the first 100 integers.

5054 = 555 + 0 + 55 + 4444.

5055 has exactly the same digits in 3 different bases.

5083 is an icosahedral number.

5087 has an eleventh root whose decimal part starts with the digits 1-9 in

some order.

5096 is the number of possible rook moves on a 14×14 chessboard.

5100 is divisible by its reverse.

5103 and its successor are both divisible by 4th powers.

5104 is the smallest number that can be written as the sum of 3 cubes in 3

ways.

5120 is the number of edges in a 10 dimensional hypercube.

5130 is a value of n for which φ(n) and σ(n) are square.

5141 is the only four digit number that is reversed in hexadecimal.

5142 is the sum of its proper divisors that contain the digit 7.

5143 = 555 + 111 + 4444 + 33.

5146 has a base 3 representation that begins with its base 7 representation.

5152 is the number of legal rook moves in chess.

5160 = 5! + (1+6)! + 0.

5161 = 5! + (1+6)! + 1!

5162 = 5! + (1+6)! + 2.

5163 = 5! + (1+6)! + 3.

5164 = 5! + (1+6)! + 4.

5165 = 5! + (1+6)! + 5.

5166 = 5! + (1+6)! + 6.

5167 = 5! + (1+6)! + 7.

5168 has a square root that has 4 8's immediately after the decimal point.

5169 = 5! + (1+6)! + 9.

5174 has a 4th power containing only 4 different digits.

5183 is the product of twin primes.

5187 is the only number n known for which φ(n-1) = φ(n) = φ(n+1).

5200 is divisible by its reverse.

5211 has a square root whose decimal part starts with the digits 1-9 in some

order.

5229 uses the same digits as φ(5229).

5244 is the sum of consecutive squares in 2 ways.

5252 is the maximum number of regions space can be divided into by 26

spheres.

5256 can be written as the sum of 2, 3, 4, or 5 cubes.

5258 has a base 8 representation which is the reverse of its base 7

representation.

5265 is a Rhonda number.

5269 is the number of binary rooted trees with 18 vertices.

5271 is a value of n for which 2n and 7n together use each digit exactly

once.

5274 is the sum of its proper divisors that contain the digit 7.

5282 is the number of different arrangements (up to rotation and reflection)

of 8 non-attacking rooks on a 8×8 chessboard.

5284 and the two numbers before it and after it are all products of exactly

3 primes.

5292 is a Kaprekar number.

5306 is the smallest number whose 9th power starts with 4 identical digits.

5312 is the index of a prime Woodall number.

5327 is a value of n for which 2n and 7n together use each digit exactly

once.

5332 is a Kaprekar constant in base 3.

5340 is an octahedral number.

5346 = (198)(27) and each digit is contained in the equation exactly once.

5349 = 12345 in base 8.

5355 = 289 + 290 + . . . + 306 = 307 + 308 + . . . + 323.

5364 is a value of n for which 3n and 7n together use each digit exactly

once.

5367 uses the same digits as φ(5367).

5383 is the number of triangles of any size contained in the triangle of

side 27 on a triangular grid.

5387 is the largest known number n so that 23n - 22n is prime.

5390 is the number of ways to 7-color the faces of a cube.

5392 is a Leyland number.

5399 has a cube whose digits occur with the same frequency.

5400 is divisible by its reverse.

5412 is a value of n so that n(n+4) is a palindrome.

5418 is a value of n for which n and 7n together use each digit 1-9 exactly

once.

5419 is the largest known number n so that 33n - 32n is prime.

5432 has digits in arithmetic sequence.

5434 is the sum of consecutive squares in 2 ways.

5439 is a Rhonda number.

5456 and its reverse are tetrahedral numbers.

5460 is the largest order of a permutation of 32 or 33 elements.

5472 has a base 3 representation that ends with its base 4 representation.

5473 has a base 3 representation that ends with its base 4 representation.

5474 is a stella octangula number.

5477 and its reverse are both one more than a square.

5482 is the number of 3×3 sliding puzzle positions that require exactly 16

moves to solve starting with the hole in the center.

5487 is the maximum number of pieces a torus can be cut into with 31 cuts.

5489 is the maximum number of regions a cube can be cut into with 32 cuts.

5501 is the largest known number n so that 93n - 92n is prime.

5509 is the number of multigraphs with 8 vertices and 9 edges.

5513 is the number of self-avoiding walks of length 10.

5525 is the smallest number that can be written as the sum of 2 squares in 6

ways.

5530 is a hexagonal pyramidal number.

5536 is the 16th tetranacci number.

5551 is the number of trees on 17 vertices with diameter 6.

5555 is a repdigit.

5564 is an amicable number.

5566 is a pentagonal pyramidal number.

5600 is the number of self-complementary graphs with 13 vertices.

5602 = 22222 in base 7.

5604 is the number of partitions of 30.

5610 is divisible by its reverse.

5616 is the order of a non-cyclic simple group.

5620 is the smallest composite number which remains composite when preceded

or followed by any digit.

5637 uses the same digits as φ(5637).

5638 is the number of 3×3 sliding puzzle positions that require exactly 17

moves to solve starting with the hole in a corner.

5651 is a number n for which n, n+2, n+6, and n+8 are all prime.

5664 is a Rhonda number.

5670 is a value of n for which φ(n) and σ(n) are square.

5671 is a triangular number that is the product of two primes.

5673 is the smallest number whose 6th power starts with 5 identical digits.

5678 has digits in arithmetic sequence.

5682 is the sum of its proper divisors that contain the digit 4.

5693 = 5555 + 6 + 99 + 33.

5694 = 17082 / 3, and each digit from 0-9 is contained in the equation

exactly once.

5696 is the number of ways to 16-color the faces of a tetrahedron.

5698 is the smallest number whose 8th power starts with 5 identical digits.

5700 is divisible by its reverse.

5714 is the number of lattice points that are within 1/2 of a sphere of

radius 21 centered at the origin.

5718 is the number of partitions of 54 into distinct parts.

5719 is a Zeisel number.

5723 has the property that its square starts with its reverse.

5739 is a value of n for which 5n and 7n together use each digit exactly

once.

5740 = 7777 in base 9.

5741 is the 11th Pell number.

5742 is a value of n for which 5n and 8n together use each digit exactly

once.

5749 is the largest known number n so that 78n - 77n is prime.

5767 is the product of two consecutive primes.

5768 is the 16th tribonacci number.

5770 is a value of n for which φ(n) and σ(n) are square.

5775 is a betrothed number.

5776 is the square of the last half of its digits.

5777 is the smallest number (besides 1) which is not the sum of a prime and

twice a square.

5778 is the largest Lucas number which is also a triangular number.

5784 = 555 + 777 + 8 + 4444.

5786 = 5555 + 77 + 88 + 66.

5795 is a value of n such that the nth Cullen number is prime.

5796 = (138)(42) and each digit is contained in the equation exactly once.

5798 is the 11th Motzkin number.

5814 = 19P3.

5817 = 34902 / 6, and each digit from 0-9 is contained in the equation

exactly once.

5822 is the number of conjugacy classes in the automorphism group of the 16

dimensional hypercube.

5823 and its triple contain every digit from 1-9 exactly once.

5824 can be written as the difference between two positive cubes in more

than one way.

5830 is an abundant number that is not the sum of some subset of its

divisors.

5832 is the cube of the sum of its digits.

5842 is a Padovan number.

5851 is the only prime so that it, its square, and its cube all have the

same sum of digits.

5857 is the largest known number n so that 51n - 50n is prime.

5859 can be written as the difference between two positive cubes in more

than one way.

5872 = 5555 + 88 + 7 + 222.

5877 is a value of n for which 5n and 8n, or 8n and 9n, together use each

digit exactly once.

5880 is the Stirling number of the second kind S(10,7).

5886 is a value of n for which 3n and 5n together use each digit exactly

once.

5890 is a heptagonal pyramidal number.

5904 has a square comprised of the digits 1-8.

5906 is the smallest number which is the sum of 2 rational 4th powers but is

not the sum of two integer 4th powers.

5909 is the number of symmetric plane partitions of 32.

5913 = 1! + 2! + 3! + 4! + 5! + 6! + 7!

5914 = 0! + 1! + 2! + 3! + 4! + 5! + 6! + 7!

5915 is the sum of consecutive squares in 2 ways.

5923 is the largest n so that Q(√n) has class number 7.

5929 is a square which is also the sum of 11 consecutive squares.

5934 is a value of n for which 5n and 7n together use each digit exactly

once.

5939 is the largest known number n so that 77n - 76n is prime.

5940 is divisible by its reverse.

5943 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.

5963 = 5555 + 9 + 66 + 333.

5967 is a value of n for which 6n and 7n together use each digit exactly

once.

5968 has a square which uses the digits 0-7 each exactly once.

5972 is the smallest number that appears in its factorial 8 times.

5974 is the number of connected planar graphs with 8 vertices.

5976 is a value of n for which n and 7n together use each digit 1-9 exactly

once.

5982 is the number of lattice points that are within 1/2 of a sphere of

radius 22 centered at the origin.

5984 = 34C3.

5985 = 21C4.

5986 and its prime factors contain every digit from 1-9 exactly once.

5993 is the largest number known which is not the sum of a prime and twice a

square.

5994 is the number of lattices on 10 unlabeled nodes.

5995 is a palindromic triangular number.

5996 is a truncated tetrahedral number.

6001 has a cube that is a concatenation of other cubes.

6003 has a square with the first 3 digits the same as the next 3 digits.

6006 is the smallest palindrome with 5 different prime factors.

6008 = 14C6 + 14C0 + 14C0 + 14C8.

6012 has a square with the last 3 digits the same as the 3 digits before

that.

6014 has a square that is formed by 3 squares that overlap by 1 digit.

6016 is the maximum number of pieces a torus can be cut into with 32 cuts.

6018 is the maximum number of regions a cube can be cut into with 33 cuts.

6020 is the number of Hamiltonian graphs with 8 vertices.

6021 has a square that is formed by 3 squares that overlap by 1 digit.

6048 is the order of a non-cyclic simple group.

6072 is the order of a non-cyclic simple group.

6077 has a square with the last 3 digits the same as the 3 digits before

that.

6084 is the sum of the first 12 cubes.

6093 is a value of n for which 3n and 5n together use each digit exactly

once.

6095 is a rhombic dodecahedral number.

6097 is an hexagonal prism number.

6099 concatenated with its successor is square.

6102 is the largest number n known where φ(n) is the the reverse of n.

6106 is a value of n for which 2φ(n) = φ(n+1).

6107 is a Perrin number.

6111 is a value of n for which σ(n-1) = σ(n+1).

6119 is a centered cube number.

6128 is a betrothed number.

6133 is the largest known number n so that 80n - 79n is prime.

6141 is a Kaprekar constant in base 2.

6144 = 16!!!!.

6145 is a Friedman number.

6163 is the largest known number n so that 62n - 61n is prime.

6174 is the Kaprekar constant for 4-digit numbers.

6175 is the number of regions formed when all diagonals are drawn in a

regular 21-gon.

6176 is the last 4-digit sequence to appear in the decimal expansion of π.

6179 is a value of n for which 4n and 5n together use each digit exactly

once.

6181 is an octahedral number.

6188 = 17C5.

6194 is the number of ways to place a non-attacking white and black pawn on

a 10×10 chessboard.

6196 is the number of regions the complex plane is cut into by drawing lines

between all pairs of 21st roots of unity.

6200 is a harmonic divisor number.

6201 is the sum of the first 26 squares.

6211 is a Cuban prime.

6216 has a square with the first 3 digits the same as the next 3 digits.

6219 is a value of n for which 4n and 5n together use each digit exactly

once.

6220 = 44444 in base 6.

6221 = 666 + 2222 + 2222 + 1111.

6223 = 666 + 2222 + 2 + 3333.

6225 = 666 + 2 + 2 + 5555.

6232 is an amicable number.

6237 is a number whose sum of squares of the divisors is a square.

6248 is the smallest number with the property that its first 8 multiples

contain the digit 4.

6249 is the smallest number with the property that its first 10 multiples

contain the digit 4.

6250 is a Leyland number.

6257 is the number of essentially different ways to dissect a 20-gon into 9

quadrilaterals.

6267 is the number of 15-iamonds with holes.

6274 has a cube whose digits occur with the same frequency.

6279 is the number of subsequences of {1,2,3,...14} in which every odd

number has an even neighbor.

6296 has a square with the first 3 digits the same as the next 3 digits.

6297 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

6300 is divisible by its reverse.

6307 is the largest n so that Q(√n) has class number 8.

6312 is the sum of its proper divisors that contain the digit 5.

6318 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

6327 = 324 + 325 + . . . + 342 = 343 + 344 + . . . + 360.

6348 is a pentagonal pyramidal number.

6368 is an amicable number.

6374 is a value of n for which 4n and 5n together use each digit exactly

once.

6375 has a square with the first 3 digits the same as the next 3 digits.

6378 is the number of partitions of 55 into distinct parts.

6380 is a value of n for which n! + 1 is prime.

6384 is an icosahedral number.

6389 is the number of functional graphs on 11 vertices.

6391 is a hexagonal pyramidal number.

6399 and its successor are both divisible by 4th powers.

6400 is a square whose digits are non-increasing.

6403 has a square with the first 3 digits the same as the last 3 digits.

6404 is a value of n for which n!! - 1 is prime.

6435 = 15C7.

6443 has a cube whose digits occur with the same frequency.

6444 is the smallest number whose 5th power starts with 5 identical digits.

6455 is the smallest value of n for which the nth prime begins with the

digits of n.

6456 is a value of n for which the nth prime begins with the digits of n.

6457 is a value of n for which the nth prime begins with the digits of n.

6459 is a value of n for which the nth prime begins with the digits of n.

6460 is a value of n for which the nth prime begins with the digits of n.

6466 is the largest known value of n for which the nth prime begins with the

digits of n.

6487 is the number of partitions of 51 in which no part occurs only once.

6489 is half again as large as the sum of its proper divisors.

6500 is a number n whose sum of the factorials of its digits is equal to

π(n).

6501 has a square whose reverse is also a square.

6510 is a number n whose sum of the factorials of its digits is equal to

π(n).

6511 is a number n whose sum of the factorials of its digits is equal to

π(n).

6521 is a number n whose sum of the factorials of its digits is equal to

π(n).

6523 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

6524 has the property that its square starts with its reverse.

6526 is the smallest number whose 10th power contains exactly the same

digits as another 10th power.

6527 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

6534 is a value of n for which 3n and 7n together use each digit exactly

once.

6545 and its reverse are tetrahedral numbers.

6543 has a square root that has 4 8's immediately after the decimal point.

6556 is the largest palindrome that can be made using 5 digits and the 4

arithmetic operations.

6557 is the product of two consecutive primes.

6560 is the smallest number n where n and n+1 are both products of 7 or more

primes.

6561 = 38.

6569 is a value of n for which one less than the product of the first n

primes is prime.

6572 is the number of 9-hexes.

6578 is the smallest number which can be written as the sum of 3 4th powers

in 2 ways.

6580 is the maximum number of regions a cube can be cut into with 34 cuts.

6588 is the number of sided 12-iamonds.

6593 = 6 + 5555 + 999 + 33.

6594 is a value of n for which 5n and 7n together use each digit exactly

once.

6596 has a square comprised of the digits 0-7.

6601 is a Carmichael number.

6602 is the number of lattice points that are within 1/2 of a sphere of

radius 23 centered at the origin.

6603 is a number whose square and cube use different digits.

6608 is the maximum number of regions space can be divided into by 28

spheres.

6611 is a value of n such that the nth Cullen number is prime.

6620 is the number of 11-ominoes that tile the plane.

6630 is the number of triangles of any size contained in the triangle of

side 29 on a triangular grid.

6636 has exactly the same digits in 3 different bases.

6643 is the smallest number which is palindromic in bases 2 and 3.

6653, when concatenated with 4 less than itself, is square.

6666 is a repdigit.

6667 is the number of self-dual planar graphs with 24 edges.

6668 is the number of trees on 21 vertices with diameter 5.

6680 = 6666 + 6 + 8 + 0.

6681 = 6666 + 6 + 8 + 1.

6682 = 6666 + 6 + 8 + 2.

6683 = 6666 + 6 + 8 + 3.

6684 = 6666 + 6 + 8 + 4.

6685 = 6666 + 6 + 8 + 5.

6686 = 6666 + 6 + 8 + 6.

6687 = 6666 + 6 + 8 + 7.

6688 = 6666 + 6 + 8 + 8.

6689 = 6666 + 6 + 8 + 9.

6720 = 8P5.

6723 is a value of n for which 3n and 8n together use each digit exactly

once.

6726 is the 10th Pell-Lucas number.

6729 and its double together use each of the digits 1-9 exactly once.

6735 is a stella octangula number.

6736 is the number of 3×3 sliding puzzle positions that require exactly 17

moves to solve starting with the hole in the center.

6742 has a square where the first 6 digits alternate.

6765 is the 20th Fibonacci number.

6769 is the Stirling number of the first kind s(8,4).

6772 = 6666 + 7 + 77 + 22.

6779 = 6666 + 7 + 7 + 99.

6788 is the smallest number with multiplicative persistence 6.

6789 is the largest 4-digit number with increasing digits.

6792 and its double together use each of the digits 1-9 exactly once.

6819 = 20457 / 3, and each digit from 0-9 is contained in the equation

exactly once.

6820 is the number of regions formed when all diagonals are drawn in a

regular 23-gon.

6822 uses the same digits as φ(6822).

6840 is the number of ways to place 2 non-attacking kings on a 11×11

chessboard.

6842 is the number of partitions of 31.

6849 is a value of n for which 2n and 3n together use each digit exactly

once.

6853 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.

6859 = 193.

6860 is a heptagonal pyramidal number.

6864 = 6666 + 88 + 66 + 44.

6867 can be written as the sum of 2, 3, 4, or 5 cubes.

6879 is the number of planar partitions of 15.

6880 is a vampire number.

6888 has a square with 3/4 of the digits are the same.

6889 is a strobogrammatic square.

6895 is a value of n for which 2n and 7n together use each digit exactly

once.

6902 is the number of Hamiltonian paths of a 3×10 rectangle graph.

6903 is a value of n for which σ(n-1) = σ(n+1).

6905 has a fifth root whose decimal part starts with the digits 1-9 in some

order.

6912 = (6) (9) (1) (2)7.

6918 = 20754 / 3, and each digit from 0-9 is contained in the equation

exactly once.

6922 is the number of polycubes containing 8 cubes.

6927 and its double together use each of the digits 1-9 exactly once.

6930 is the square root of a triangular number.

6939 is a value of n for which 3n and 5n together use each digit exactly

once.

6940 is the sum of its proper divisors that contain the digit 3.

6941 has a square with the first 3 digits the same as the last 3 digits.

6942 is the number of labeled topologies with 5 elements.

6951 has exactly the same digits in 3 different bases.

6952 = 1738 * 4 and each digit from 1-9 is contained in the equation exactly

once.

6953 = 66 + 999 + 5555 + 333.

6959 is the largest known number n so that 90n - 89n is prime.

6966 is the number of planar graphs with 8 vertices.

6984 can be written as the sum of 2, 3, 4, or 5 cubes.

6991 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

6996 is a palindrome n so that n(n+8) is also palindromic.

7014 has a square with the last 3 digits the same as the 3 digits before

that.

7015 has a cube root whose decimal part starts with the digits 1-9 in some

order.

7032 is the number of ternary square-free words of length 24.

7039 = 28156 / 4, and each digit from 0-9 is contained in the equation

exactly once.

7043 is the largest known number n so that 56n - 55n is prime.

7056 is a square that is the product of two triangular numbers.

7057 is a Cuban prime.

7073 is a Leyland number.

7102 is the index of a Fibonacci number whose first 9 digits are the digits

1-9 rearranged.

7106 is an octahedral number.

7108 is the number of partitions of 56 into distinct parts.

7123 is the number of 2-connected graphs with 8 vertices.

7130 is the number of lattice points that are within 1/2 of a sphere of

radius 24 centered at the origin.

7140 is the largest number which is both triangular and tetrahedral.

7145 has a square with the first 3 digits the same as the next 3 digits.

7152 has a square with the first 3 digits the same as the next 3 digits.

7159 has a square with the first 3 digits the same as the next 3 digits.

7161 is a Kaprekar constant in base 2.

7170 is a value of n for which σ(n-1) = σ(n+1).

7174 is the maximum number of pieces a torus can be cut into with 34 cuts.

7176 is the maximum number of regions a cube can be cut into with 35 cuts.

7192 is an abundant number that is not the sum of some subset of its

divisors.

7200 is a pentagonal pyramidal number.

7219 is the largest known number n so that 29n - 28n is prime.

7225 is the number of ways to 17-color the faces of a tetrahedron.

7230 is the sum of consecutive squares in 2 ways.

7235 is a value of n for which 4n and 5n together use each digit exactly

once.

7236 uses the same digits as φ(7236).

7245 appears inside its 4th power.

7254 = (186)(39) and each digit is contained in the equation exactly once.

7256 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.

7269 and its double together use each of the digits 1-9 exactly once.

7272 is a Kaprekar number.

7281 is a value of n for which 3n and 7n together use each digit exactly

once.

7293 and its double together use each of the digits 1-9 exactly once.

7295 is a value of n for which 4n and 5n together use each digit exactly

once.

7306 is the smallest number whose 7th power starts with 7 identical digits.

7311 is the number of symmetric plane partitions of 33.

7314 is the smallest number so that it and its successor are both products

of 4 primes.

7315 = 22C4.

7318 is the number of functions from 10 unlabeled points to themselves.

7320 is the number of triangles of any size contained in the triangle of

side 30 on a triangular grid.

7322 is the number of 3×3 sliding puzzle positions that require exactly 17

moves to solve starting with the hole on a side.

7329 and its double together use each of the digits 1-9 exactly once.

7331 is the largest known number n so that 20n - 19n is prime.

7337 is a hexagonal pyramidal number.

7344 is a value of n for which 4n and 7n together use each digit exactly

once.

7351 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

7356 is a value of n for which 5n and 7n together use each digit exactly

once.

7359 is the number of 3×3 sliding puzzle positions that require exactly 27

moves to solve starting with the hole on a side.

7360 can be written as the product of a number and its reverse in 2

different ways.

7361 is the number of self-avoiding walks in a quadrant of length 11.

7366 is the maximum number of regions space can be divided into by 29

spheres.

7371 has a base 2 representation that begins with its base 9 representation.

7381 = 11111 in base 9.

7385 is a Keith number.

7387 is the product of two consecutive primes.

7396 has a fourth root whose decimal part starts with the digits 1-9 in some

order.

7410 = 361 + 362 + . . . + 380 = 381 + 382 + . . . + 399.

7421 is a value of n for which 4n and 5n together use each digit exactly

once.

7422 is the sum of its proper divisors that contain the digit 7.

7429 is the product of 3 consecutive primes.

7436 is the number of 6×6 alternating sign matrices.

7448 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

7465 = 54321 in base 6.

7471 is a centered cube number.

7489 is the largest known number n so that 59n - 58n is prime.

7490 has a square with the last 3 digits the same as the 3 digits before

that.

7491 has a base 8 representation which is the reverse of its base 7

representation.

7494 is the sum of its proper divisors that contain the digit 4.

7496 = 777 + 44 + 9 + 6666.

7509 has a sixth root whose decimal part starts with the digits 1-9 in some

order.

7512 is the sum of its proper divisors that contain the digit 5.

7525 has a square with the last 3 digits the same as the 3 digits before

that.

7531 has digits in arithmetic sequence.

7532 has a square comprised of the digits 0-7.

7542 is a value of n for which 4n and 7n together use each digit exactly

once.

7549 is the largest known prime p where no numbers of the form p-n2 are

prime.

7559 is the largest known number n so that 15n - 14n is prime.

7560 is the smallest number with 64 divisors.

7574 is the sum of consecutive squares in 2 ways.

7581 is the number of monotone Boolean functions of 5 variables.

7586 = 777 + 55 + 88 + 6666.

7590 is a number whose sum of divisors is a 4th power.

7595 is the number of simplicial polyhedra with 12 vertices.

7614 is a value of n for which n and 7n together use each digit 1-9 exactly

once.

7617 is a hexanacci number.

7620 is the number of multigraphs with 5 vertices and 14 edges.

7629 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

7632 is a value of n for which 5n and 6n together use each digit exactly

once.

7647 is a Keith number.

7650 can be written as the product of a number and its reverse in 2

different ways.

7654 has digits in arithmetic sequence.

7658 is an hexagonal prism number.

7663 is the product of two primes which are reverses of each other.

7665 is a Kaprekar constant in base 2.

7672 = 777 + 6666 + 7 + 222.

7673 is the smallest number with the property that its first 8 multiples

contain the digit 3.

7679 = 7 + 6666 + 7 + 999.

7680 is the number of possible rook moves on a 16×16 chessboard.

7683 is a truncated tetrahedral number.

7686 is a value of n for which 7n and 9n together use each digit exactly

once.

7692 and its double together use each of the digits 1-9 exactly once.

7693 is a value of n for which the sum of the first n primes is a

palindrome.

7695 and its successor are both divisible by 4th powers.

7698 has a square with the first 3 digits the same as the next 3 digits.

7699 is the largest known number n so that 11n - 10n is prime.

7700 is a value of n for which 2φ(n) = φ(n+1).

7710 is the number of degree 17 irreducible polynomials over GF(2).

7713 is a value of n for which 4n and 9n together use each digit exactly

once.

7714 is the sum of the first 28 squares.

7727 is the index of a Fibonacci number whose first 9 digits are the digits

1-9 rearranged.

7732 and the two numbers before it and after it are all products of exactly

3 primes.

7734 is the sum of its proper divisors that contain the digit 8.

7739 is a Padovan number.

7741 is the number of trees with 15 vertices.

7744 is the only square known with no isolated digits.

7745 and its reverse are both one more than a square.

7755 is the index of a prime Woodall number.

7770 = 37C3.

7772 has a square root whose decimal part starts with the digits 1-9 in some

order.

7775 = 55555 in base 6.

7776 is a 5th power whose digits are non-increasing.

7777 is a Kaprekar number.

7785 is a value of n for which 5n and 6n together use each digit exactly

once.

7800 is the order of a non-cyclic simple group.

7805 is the maximum number of pieces a torus can be cut into with 35 cuts.

7807 is the maximum number of regions a cube can be cut into with 36 cuts.

7810 has the property that its square is the concatenation of two

consecutive numbers.

7812 = 222222 in base 5.

7821 is a value of n for which 2n and 9n together use each digit exactly

once.

7824 is a value of n for which 5n and 7n together use each digit exactly

once.

7825 is a rhombic dodecahedral number.

7851 = 7777 + 8 + 55 + 11.

7852 = 1963 * 4, and each digit from 1-9 is contained in the equation

exactly once.

7854 is a number whose sum of divisors is a 4th power.

7856 = 7777 + 8 + 5 + 66.

7884 is a value of n for which 2n and 5n together use each digit exactly

once.

7890 is an icosahedral number.

7895 is the number of multigraphs with 6 vertices and 11 edges.

7905 is a Kaprekar constant in base 2.

7909 is a Keith number.

7913 is a value of n for which σ(n-1) = σ(n+1).

7917 is the number of partitions of 57 into distinct parts.

7920 is the order of the smallest sporadic group.

7923 and its double together use each of the digits 1-9 exactly once.

7928 is a Friedman number.

7931 is a heptagonal pyramidal number.

7932 and its double together use each of the digits 1-9 exactly once.

7936 is the 9th Euler number.

7941 = 7777 + 9 + 44 + 111.

7942 = 7777 + 99 + 44 + 22.

7946 = 7777 + 99 + 4 + 66.

7956 is a value of n for which n and 4n together use each digit 1-9 exactly

once.

7969 has a square that is formed by 3 squares that overlap by 1 digit.

7980 is the smallest number whose divisors contain every digit at least 7

times.

7988 = 11 * 22 * 33.

7992 can be written as the difference between two positive cubes in more

than one way.

7993 is one less than twice its reverse.

8000 is the smallest cube which is also the sum of 4 consecutive cubes.

8001 is a Kaprekar constant in base 2.

8004 has a square with the first 3 digits the same as the next 3 digits.

8008 = 16C6.

8010 uses the same digits as π(8010).

8016 has a square with the last 3 digits the same as the 3 digits before

that.

8022 uses the same digits as φ(8022).

8026 is the number of planar partitions of 19.

8034 is the number of lattice points that are within 1/2 of a sphere of

radius 25 centered at the origin.

8042 is the largest number known which cannot be written as a sum of 7 or

fewer cubes.

8051 is the number of partitions of 52 in which no part occurs only once.

8056 is the number of triangles of any size contained in the triangle of

side 31 on a triangular grid.

8071 is the number of connected graphs with 11 edges.

8080 has a square root that has 4 8's immediately after the decimal point.

8082 has a square comprised of the digits 1-8.

8090 is a Perrin number.

8092 is a Friedman number.

8100 is divisible by its reverse.

8103 is the closest integer to e9.

8119 is an NSW number.

8125 is the smallest number that can be written as the sum of 2 squares in 5

ways.

8128 is the 4th perfect number.

8136 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

8149 is a value of n for which 2n and 7n together use each digit exactly

once.

8169 = 24507 / 3, and each digit from 0-9 is contained in the equation

exactly once.

8176 is a stella octangula number.

8179 is a value of n for which 4n and 5n together use each digit exactly

once.

8180 is the maximum number of regions space can be divided into by 30

spheres.

8184 has exactly the same digits in 3 different bases.

8190 is a harmonic divisor number.

8191 is a Mersenne prime.

8192 is the smallest 13th power (besides 1).

8198 is the index of a Fibonacci number whose first 9 digits are the digits

1-9 rearranged.

8200 = 8 + 213 + 0 + 0.

8201 = 8 + 213 + 0 + 1.

8202 = 8 + 213 + 0 + 2.

8203 = 8 + 213 + 0 + 3.

8204 = 8 + 213 + 0 + 4.

8205 = 8 + 213 + 0 + 5.

8206 = 8 + 213 + 0 + 6.

8207 = 8 + 213 + 0 + 7.

8208 = 84 + 24 + 04 + 84.

8209 = 8 + 213 + 0 + 9.

8219 is a value of n for which 4n and 5n together use each digit exactly

once.

8221 has a base 3 representation that begins with its base 6 representation.

8226 is the sum of its proper divisors that contain the digit 4.

8256 is the number of different arrangements (up to rotation and reflection)

of 30 non-attacking bishops on a 16×16 chessboard.

8265 has a seventh root whose decimal part starts with the digits 1-9 in

some order.

8269 is a Cuban prime.

8281 is the only 4-digit square whose two 2-digit pairs are consecutive.

8283 has a base 8 representation which is the reverse of its base 7

representation.

8297 is the largest known number n so that 81n - 80n is prime.

8299 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

8303 = 12345 in base 9.

8338 is a value of n so that n(n+4) is a palindrome.

8342 is the number of partitions of 53 in which no part occurs only once.

8349 is the number of partitions of 32.

8361 is a Leyland number.

8372 is a hexagonal pyramidal number.

8375 is the smallest number which has equal numbers of every digit in bases

2 and 6.

8378 has a tenth root whose decimal part starts with the digits 1-9 in some

order.

8379 is a value of n for which 5n and 8n together use each digit exactly

once.

8384 is the maximum number of 13th powers needed to sum to any number.

8392 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.

8400 is the number of legal queen moves in chess.

8403 = 33333 in base 7.

8415 is the smallest number which has equal numbers of every digit in bases

3 and 6.

8436 = 38C3.

8447 is the largest known number n so that 45n - 44n is prime.

8451 is the number of 3×3 matrices in base 3 with determinant 0.

8459 is a value of n so that n(n+4) is a palindrome.

8461 is the smallest number whose 9th power starts with 5 identical digits.

8467 has a ninth root whose decimal part starts with the digits 1-9 in some

order.

8469 is a value of n for which 2n and 3n together use each digit exactly

once.

8470 is the number of conjugacy classes in the automorphism group of the 17

dimensional hypercube.

8472 is the maximum number of pieces a torus can be cut into with 36 cuts.

8474 is the maximum number of regions a cube can be cut into with 37 cuts.

8484 is the reciprocal of the sum of the reciprocals of 13332 and its

reverse.

8486 = 888 + 44 + 888 + 6666.

8510 is a value of n for which the sum of the first n primes is a

palindrome.

8515 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

8526 is a Rhonda number.

8538 is the sum of its proper divisors that contain the digit 4.

8541 is a value of n so that n(n+6) is a palindrome.

8555 is the sum of the first 29 squares.

8558 is a Schröder number.

8559 has a square comprised of the digits 1-8.

8562 is the sum of its proper divisors that contain the digit 4.

8568 = 18C5.

8576 can be written as the sum of 2, 3, 4, or 5 cubes.

8578 appears inside its 4th power.

8586 has exactly the same digits in 3 different bases.

8606 is the number of lattice points that are within 1/2 of a sphere of

radius 26 centered at the origin.

8610 = 400 + 401 + . . . + 420 = 421 + 422 + . . . + 440.

8614 and its prime factors contain every digit from 1-9 exactly once.

8627 is a value of n for which 2n and 7n together use each digit exactly

once.

8631 is a value of n for which 3n and 7n together use each digit exactly

once.

8633 is the product of two consecutive primes.

8642 has digits in arithmetic sequence.

8649 is a value of n for which 2n and 7n together use each digit exactly

once.

8658 is the sum of the first 4 perfect numbers.

8664 = 888 + 6666 + 666 + 444.

8666 has a ninth root whose decimal part starts with the digits 1-9 in some

order.

8670 is a value of n for which n!! - 1 is prime.

8680 has a base 5 representation that ends with its base 7 representation.

8681 has a base 5 representation that ends with its base 7 representation.

8682 has a base 5 representation that ends with its base 7 representation.

8683 has a base 5 representation that ends with its base 7 representation.

8684 has a base 5 representation that ends with its base 7 representation.

8688 is the number of possible configurations of pegs (up to symmetry) after

26 jumps in solitaire.

8712 is 4 times its reverse.

8714 is the number of ways 24 people around a round table can shake hands in

a non-crossing way, up to rotation.

8721 is a value of n for which φ(n) and σ(n) are square.

8732 has exactly the same digits in 3 different bases.

8736 is the smallest number that appears in its factorial 10 times.

8743 is a number whose sum of divisors is a 4th power.

8751 has a fourth root whose decimal part starts with the digits 1-9 in some

order.

8753 = 88 + 7777 + 555 + 333.

8758 = 88 + 7777 + 5 + 888.

8763 and its successor have the same digits in their prime factorization.

8765 has digits in arithmetic sequence.

8772 is the sum of the first 8 4th powers.

8778 is a palindromic triangular number.

8784 is a value of n for which 2n and 5n together use each digit exactly

once.

8796 is a value of n for which 5n and 7n together use each digit exactly

once.

8808 is the number of partitions of 58 into distinct parts.

8816 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

8826 is the sum of its proper divisors that contain the digit 4.

8829 is a value of n for which 6n and 7n together use each digit exactly

once.

8833 = 882 + 332.

8839 is the largest known number n so that 60n - 59n is prime.

8840 is the number of triangles of any size contained in the triangle of

side 32 on a triangular grid.

8855 = 23C4.

8867 is the largest known number n so that 30n - 29n is prime.

8874 has a square that is the concatenation of two consecutive even numbers.

8888 is a repdigit.

8892 is a betrothed number.

8910 is divisible by its reverse.

8911 is a Carmichael number.

8922 is the sum of its proper divisors that contain the digit 4.

8930 = 8888 + 9 + 33 + 0.

8931 = 8888 + 9 + 33 + 1.

8932 = 8888 + 9 + 33 + 2.

8933 = 8888 + 9 + 33 + 3.

8934 = 8888 + 9 + 33 + 4.

8935 = 8888 + 9 + 33 + 5.

8936 = 8888 + 9 + 33 + 6.

8937 = 8888 + 9 + 33 + 7.

8938 = 8888 + 9 + 33 + 8.

8939 = 8888 + 9 + 33 + 9.

8950 has a fourth root whose decimal part starts with the digits 1-9 in some

order.

8964 is the smallest number with the property that its first 6 multiples

contain the digit 8.

8970 = 8 + 94 + 74 + 0.

8971 = 8 + 94 + 74 + 1.

8972 = 8 + 94 + 74 + 2.

8973 = 8 + 94 + 74 + 3.

8974 = 8 + 94 + 74 + 4.

8975 = 8 + 94 + 74 + 5.

8976 = 8 + 94 + 74 + 6.

8977 = 8 + 94 + 74 + 7.

8978 = 8 + 94 + 74 + 8.

8979 = 8 + 94 + 74 + 9.

8982 uses the same digits as φ(8982).

8989 is a Delannoy number.

8991 is the smallest number so that it and its successor are both the

product of a prime and the 5th power of a prime.

9002 is a value of n so that n(n+7) is a palindrome.

9009 is a centered cube number.

9011 has a square that is the concatenation of two consecutive odd numbers.

9012 is the sum of its proper divisors that contain the digit 5.

9013 is the largest known number n so that 65n - 64n is prime.

9016 is the number of perfect squared rectangles of order 16.

9018 has a square with the last 3 digits the same as the 3 digits before

that.

9024 is the number of regions formed when all diagonals are drawn in a

regular 24-gon.

9025 is a Friedman number.

9037 is a value of n for which 2n and 7n together use each digit exactly

once.

9045 is the number of ways to 18-color the faces of a tetrahedron.

9048 is the number of regions the complex plane is cut into by drawing lines

between all pairs of 24th roots of unity.

9052 is the maximum number of regions space can be divided into by 31

spheres.

9066 is the number of lattice points that are within 1/2 of a sphere of

radius 27 centered at the origin.

9070 has a fourth root whose decimal part starts with the digits 1-9 in some

order.

9072 has a base 2 and base 3 representation that end with its base 6

representation.

9073 has a base 2 and base 3 representation that end with its base 6

representation.

9074 has a base 3 representation that ends with its base 6 representation.

9078 has a cube whose digits occur with the same frequency.

9079 has a square that is the concatenation of two consecutive decreasing

numbers.

9086 is the number of regions formed when all diagonals are drawn in a

regular 23-gon.

9091 is the only prime known whose reciprocal has period 10.

9093 has a square with the first 3 digits the same as the next 3 digits.

9099 is the number of ways to 3-color the faces of a dodecahedron.

9101 has a square where the first 6 digits alternate.

9104 has a square with the first 3 digits the same as the next 3 digits.

9108 is a heptagonal pyramidal number.

9109 is the number of regions the complex plane is cut into by drawing lines

between all pairs of 23rd roots of unity.

9115 has a base 3 representation that begins with its base 6 representation.

9117 is a value of n for which 6n and 7n together use each digit exactly

once.

9119 is the number of symmetric plane partitions of 34.

9121 is the number of possibilities for the last 5 digits of a square.

9126 is a pentagonal pyramidal number.

9127 is the largest known number n so that 21n - 20n is prime.

9134 has a tenth root whose decimal part starts with the digits 1-9 in some

order.

9135 is a value of n for which 2n and 7n together use each digit exactly

once.

9139 = 39C3.

9152 and its successor are both divisible by 4th powers.

9153 is a value of n for which 2n and 3n together use each digit exactly

once.

9154 is a value of n for which φ(n) and σ(n) are square.

9162 is a value of n for which 5n and 8n together use each digit exactly

once.

9168 = 27504 / 3, and each digit from 0-9 is contained in the equation

exactly once.

9172 is the number of connected planar maps with 7 edges.

9174 is the sum of its proper divisors that contain the digit 5.

9176 is the maximum number of pieces a torus can be cut into with 37 cuts.

9178 is the maximum number of regions a cube can be cut into with 38 cuts.

9179 is a value of n for which φ(n) = φ(n-1) + φ(n-2).

9182 is a value of n for which 4n and 5n together use each digit exactly

once.

9183 is the number of sets of distinct positive integers with mean 8.

9185 is a value of n for which 2n and 7n together use each digit exactly

once.

9189 is the number of sided 10-ominoes.

9198 is the number of ternary square-free words of length 25.

9214 has a sixth root whose decimal part starts with the digits 1-9 in some

order.

9216 is a Friedman number.

9217 is the total number of digits of all binary numbers of length 1-10.

9224 is an octahedral number.

9233 is the number of different arrangements (up to rotation and reflection)

of 13 non-attacking queens on a 13×13 chessboard.

9234 is the number of multigraphs with 7 vertices and 10 edges.

9235 is the number of 13-iamonds.

9237 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

9240 = 22P3.

9241 is a Cuban prime.

9248 is the number of possible rook moves on a 17×17 chessboard.

9252 is the number of necklaces with 10 white and 10 black beads.

9253 is the smallest number that appears in its factorial 9 times.

9261 is a Friedman number.

9267 and its double together use each of the digits 1-9 exactly once.

9268 is a value of n for which 2φ(n) = φ(n+1).

9272 is an abundant number that is not the sum of some subset of its

divisors.

9273 and its double together use each of the digits 1-9 exactly once.

9282 is the product of three consecutive Fibonacci numbers.

9285 is the number of 16-hexes with reflectional symmetry.

9287 is the number of stretched 10-ominoes.

9288 can be written as the sum of 2, 3, 4, or 5 cubes.

9289 is a tetranacci number.

9304 = 65128 / 7, and each digit from 0-9 is contained in the equation

exactly once.

9306 is a value of n for which 3n and 5n together use each digit exactly

once.

9311 is the index of a prime Fibonacci number.

9315 is a value of n for which 2n and 3n together use each digit exactly

once.

9324 is the reciprocal of the sum of the reciprocals of 14652 and its

reverse.

9327 and its double together use each of the digits 1-9 exactly once.

9330 is the Stirling number of the second kind S(10,3).

9331 = 111111 in base 6.

9339 is a value of n for which φ(n) = φ(n-2) - φ(n-1).

9347 is a value of n for which the sum of square-free divisors of n and n+1

are the same.

9349 is the 19th Lucas number.

9350 appears inside its 4th power.

9360 is a value of n for which σ(n-1) = σ(n+1).

9362 = 22222 in base 8.

9364 is the number of connected digraphs with 5 vertices.

9367 is a value of n for which n, n+1, n+2, and n+3 have the same number of

divisors.

9373 is the number of chess positions that can be reached in only one way

after 2 moves by each player.

9374 is a value of n for which φ(σ(n)) = φ(n).

9375 has a cube that ends with those digits.

9376 is an automorphic number.

9377 is a value of n for which n, 2n, 3n, and 4n all use the same number of

digits in Roman numerals.

9378 is a value of n for which 4n and 5n together use each digit exactly

once.

9382 is a value of n for which 4n and 5n together use each digit exactly

once.

9383 is the index of a Fibonacci number whose first 9 digits are the digits

1-9 rearranged.

9385 is the sum of consecutive squares in 2 ways.

9386 = 99 + 333 + 8888 + 66.

9391 has a square with the first 3 digits the same as the last 3 digits.

9393 is the number of non-isomorphic 3×3×3 Rubik cube positions that require

exactly 5 quarter turns to solve.

9394 is a value of n so that n(n+8) is a palindrome.

9396 is the number of symmetric 3×3 matrices in base 6 with determinant 0.

9403 = 65821 / 7, and each digit from 0-9 is contained in the equation

exactly once.

9407 has a seventh root whose decimal part starts with the digits 1-9 in

some order.

9408 is the number of reduced 6×6 Latin squares.

9413 has a cube whose digits occur with the same frequency.

9424 has the property that the fractional part of π9424 begins .9424....

9426 is a value of n for which 5n and 7n together use each digit exactly

once.

9431 is a number n for which n, n+2, n+6, and n+8 are all prime.

9432 is the number of 3-colored rooted trees with 6 vertices.

9436 is the smallest number whose 15th power contains exactly the same

digits as another 15th power.

9439 is the largest known number n so that 92n - 91n is prime.

9444 has a square with the first 3 digits the same as the next 3 digits.

9450 is the denominator of ζ(8) / π8.

9451 is the number of binary rooted trees with 19 vertices.

9455 is the sum of the first 30 squares.

9465 is an hexagonal prism number.

9468 is the sum of its proper divisors that contain the digit 7.

9471 is an octagonal pyramidal number.

9474 = 94 + 44 + 74 + 44.

9477 is the maximum determinant of a 13×13 matrix of 0's and 1's.

9481 is a number whose sum of divisors is a 4th power.

9489 is the closest integer to π8.

9496 is the number of 10×10 symmetric permutation matrices.

9500 is a hexagonal pyramidal number.

9504 is a betrothed number.

9513 is the smallest number without increasing digits that is divisible by

the number formed by writing its digits in increasing order.

9521 is the largest known number n so that 41n - 40n is prime.

9523 is a value of n for which 4n and 5n together use each digit exactly

once.

9529 is the number of 3×3 sliding puzzle positions that require exactly 18

moves to solve starting with the hole in a corner.

9531 is the index of a prime Woodall number.

9538 is a value of n for which 4n and 5n together use each digit exactly

once.

9542 is the number of ways to place a non-attacking white and black pawn on

a 11×11 chessboard.

9552 and the following 34 numbers are composite.

9563 = 9 + 5555 + 666 + 3333.

9564 is the number of paraffins with 10 carbon atoms.

9568 = 9 + 5 + 666 + 8888.

9576 = 19!!!!!.

9592 is the number of primes less than 100,000.

9605, when concatenated with 4 less than itself, is square.

9608 is the number of digraphs with 5 vertices.

9615 is the smallest number whose cube starts with 5 identical digits.

9616 is an icosahedral number.

9623 is the number of symmetric 10-cubes.

9625 has a square formed by inserting a block of digits inside itself.

9627 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

9629 is a value of n for which 2n and 7n together use each digit exactly

once.

9632 is the number of different arrangements of 4 non-attacking queens on a

4×14 chessboard.

9648 is a factor of the sum of the digits of 96489648.

9653 = 99 + 666 + 5555 + 3333.

9658 = 99 + 666 + 5 + 8888.

9660 is a truncated tetrahedral number.

9670 is the number of 8-digit triangular numbers.

9673 is the number of triangles of any size contained in the triangle of

side 33 on a triangular grid.

9677 is the largest known number n so that 86n - 85n is prime.

9682 is a value of n for which n!! - 1 is prime.

9689 is the exponent of a Mersenne prime.

9695 is the sum of the digits of 555.

9700 is the number of inequivalent 4-digit strings, where two strings are

equivalent if turning one upside down gives the other.

9709 has a cube whose digits occur with the same frequency.

9711 uses the same digits as π(9711).

9716 is the number of Pyramorphix puzzle positions that require exactly 5

moves to solve.

9721 is the largest prime factor of 1234567.

9723 is a value of n for which n and 5n together use each digit 1-9 exactly

once.

9726 is the smallest number in base 5 whose square contains the same digits

in the same proportion.

9728 can be written as the sum of 2, 3, 4, or 5 cubes.

9738 is the number of trees on 22 vertices with diameter 5.

9743 is the largest known number n so that 13n - 12n is prime.

9751 is the number of possible configurations of pegs (up to symmetry) after

8 jumps in solitaire.

9753 is a value of n for which 4n and 5n together use each digit exactly

once.

9754 is the number of paths between opposite corners of a 3×5 rectangle

graph.

9760 can be written as the product of a number and its reverse in 2

different ways.

9767 is the largest 4 digit prime composed of concatenating two 2 digit

primes.

9768 = 2 * 22 * 222.

9770 is the number of Hamiltonian cycles of a 4×12 rectangle graph.

9775 is a number n so that the sum of the digits of nn-1 is divisible by n.

9777 is the number of graphs on 8 vertices with no isolated vertices.

9779 has a square root that has 4 8's immediately after the decimal point.

9781 is the largest known number n so that 47n - 46n is prime.

9784 is the number of 2 state Turing machines which halt.

9789 is the smallest number that appears in its factorial 11 times.

9790 is the number of ways to place 2 non-attacking kings on a 12×12

chessboard.

9792 is the number of partitions of 59 into distinct parts.

9793 is the smallest number that can be written as the sum of 4 distinct

positive cubes in 5 ways.

9797 is the product of two consecutive primes.

9798 is a number whose sum of divisors is a 4th power.

9799 is a number whose sum of squares of the divisors is a square.

9800 is the largest 4-digit number with single digit prime factors.

9801 is 9 times its reverse.

9805 is the number of subsequences of {1,2,3,...15} in which every odd

number has an even neighbor.

9809 is a stella octangula number.

9825 is number of chess positions that can be obtained uniquely by two moves

by each player.

9828 is the order of a non-cyclic simple group.

9831 has a base 6 representation which is the reverse of its base 5

representation.

9841 = 111111111 in base 3.

9843 is the number of vertices in a Sierpinski triangle of order 8.

9855 is a rhombic dodecahedral number.

9858 is a number whose sum of divisors is a 4th power.

9862 is the number of knight's tours on a 6×6 chessboard.

9868 is the number of hydrocarbons with 10 carbon atoms.

9871 is the largest 4-digit prime with different digits.

9876 is the largest 4-digit number with different digits.

9880 = 40C3.

9883 is the largest known number n so that 72n - 71n is prime.

9888 is the number of connected graphs with 8 vertices whose complements are

also connected.

9894 is the number of 3-colored trees with 7 vertices.

9896 is the number of Pyraminx puzzle positions that require exactly 6 moves

to solve.

9901 is the only prime known whose reciprocal has period 12.

9910 is the number of fixed 9-ominoes.

9912 is the number of graceful permutations of length 14.

9918 is the maximum number of pieces a torus can be cut into with 38 cuts.

9919 can be written as the difference between two positive cubes in more

than one way.

9920 is the maximum number of regions a cube can be cut into with 39 cuts.

9928 is a value of n for which reverse(φ(n)) = φ(reverse(n)).

9929 is the number of 3×3 sliding puzzle positions that require exactly 26

moves to solve starting with the hole on a side.

9933 = 441 + 442 + . . . + 462 = 463 + 464 + . . . + 483.

9941 is the exponent of a Mersenne prime.

9944 divides the sum of the largest prime factors of the first 9944 positive

integers.

9945 = 17!!!!.

9949 is the largest known number n so that 79n - 78n is prime.

9962 is the number of lattice points that are within 1/2 of a sphere of

radius 28 centered at the origin.

9960 is the number of 3×3×3 sliding puzzle positions that require exactly 8

moves to solve.

9966 is the largest 4-digit strobogrammatic number.

9973 is the largest 4-digit prime.

9976 has a square formed by inserting a block of digits inside itself.

9984 is the maximum number of regions space can be divided into by 32

spheres.

9985 is the number of hyperbolic knots with 13 crossings.

9988 is the number of prime knots with 13 crossings.

9992 is the number of 2×2×2 Rubik cube positions that require exactly 5

moves to solve.

9995 has a square formed by inserting a block of digits inside itself.

9996 has a square formed by inserting a block of digits inside itself.

9998 is the smallest number n for which the concatenation of n, (n+1), ...

(n+21) is prime.

9999 is a Kaprekar number.

A delightful site, with great links (useful in figuring out some of the references in the text):

What's Special About This Number?

http://www.stetson.edu/~efriedma/numbers.html

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## Comments

Half the fun is just wondering how in the world you omitted so many letters at random! and wondering whether any digits were dropped in the process, too...

Posted by: Chap | Aug 12, 2007 6:40:03 PM

the BEST website on numbers is:

http://www.archimedes-lab.org/numbers/Num1_69.html

it really worths a visit...

Posted by: gongo | Apr 21, 2008 10:19:58 AM

The comments to this entry are closed.

I love this list. Some of my favorite numbers involve special properties of (1/n) and allow you to do fast calculations. Now I know more interesting things about these numbers.

7 and 23 both have the property and are infinite repeating decimals have (n-1 digit) cycle. For example:

1/7=.142857....

2/7=.285714....

3/7=.571428....

...

Also, videophysics.com is my site that addresses the voices in my head. I do lot of simple experiments with common items. Do you know what a drop a Budweiser looks like in beer? Very cool and not obvious.

Regards,

Danny

Posted by: DSS | Mar 2, 2007 4:50:26 PM