Annotated version of "What's Special About This Number?" (Part 0)

Introduction

Erich Friedman has a very nice (and deservedly popular) page called What's Special About This Number?

It does not, however, mention the sequences in the OEIS where these numbers can be found (and from where I suspect most of the entries were taken).

The present set of ten pages is a snapshot of his page as of May 23, 2010, with pointers to the corresponding entries in the OEIS. The pages are:

• Part 0: 0 to 999,
• Part 1: 1000 to 1999,
• Part 2: 2000 to 2999,
• Part 3: 3000 to 3999,
• Part 4: 4000 to 4999,
• Part 5: 5000 to 5999,
• Part 6: 6000 to 6999,
• Part 7: 7000 to 7999,
• Part 8: 8000 to 8999,
• Part 9: 9000 to 9999.

People are invited to add more pointers to these pages, by adding the appropriate A-numbers to the entries. It may be necessary to create new sequences to do this - see A158304 for an example.

To add a link to sequence A000108, for example, type A000108.

I should add that this is being done with Erich Friedman's approval.

I did not do a very good job of converting the original html format to wiki format, and in some cases you may have to refer to Erich's page to figure out the meaning or the links.

You may well find better descriptions for some numbers. If so, please send them to Erich and make the corresponding changes here. (The wiki software is complaining that these pages are too long. I decided to ignore these complaints.)

Neil Sloane

Part 0: The Numbers 0 to 999

0 is the additive identity and the empty sum (A000004)

1 is the multiplicative identity and the empty product (A000012)

2 is the only even prime (A000040). It is also the only positive integer which satisfies x + x = x ∗ x = x ^ x = x ↑↑ x = x ↑↑↑ x = ... (see Knuth's up-arrow notation). It is also the 1^st primary pseudoperfect number (A054377).

3 is the number of spatial dimensions we live in. It is also the number of regular polytopes in all dimensions larger than four (A060296)

4 is the smallest number of colors sufficient to color all planar maps (A000934, A158411)

5 is the number of Platonic solids, i.e., the number of regular polytopes in 3 dimensions (A060296(3)=5)

6 is the smallest perfect number (A000396). Also, 6 is the maximum (finite) value of A060296, as there are six regular polytopes in 4 dimensions. Among symmetric groups, only $S_{6}$ has a non-trivial outer automorphism. It is also the 2^nd primary pseudoperfect number (A054377).

7 is the smallest number of sides of a regular polygon that is not constructable by straight-edge and compass (A003401, A004169)

8 is the largest cube in the Fibonacci sequence (A000045, A000578)

9 is the maximum number of cubes that are needed to sum to any positive integer (A002376)

10 is the base of our number system

11 is the largest known multiplicative persistence (A003001, A031346)

12 is the smallest abundant number (A005101)

13 is the number of Archimedian solids

14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers (A005277)

15 is the smallest composite number n with the property that there is only one group of order n (A000001, A050384)

16 is the only number of the form x^y = y^x with x and y different integers

17 is the number of wallpaper groups

18 is the only number (other than 0) that is twice the sum of its digits (A169805, A007953)

19 is the maximum number of 4^th powers needed to sum to any number (A002377)

20 is the number of rooted trees with 6 vertices (A000081)

21 is the smallest number of distinct squares needed to tile a square (A006983)

22 is the number of partitions of 8 (A000041)

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 than its square root

25 is the smallest square that can be written as a sum of 2 (nonzero) squares (A134422). It is also the smallest composite number that is both a Lucky number (A000959) and Ludic number (A003309). Also, the smallest composite number, whose binary expansion 11001, when interpreted as a polynomial in ring GF(2)[X], (x^4 + x^3 + 1), is irreducible in that ring (A091214).

26 is the only 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 2^nd perfect number (A000396)

29 is the 7^th Lucas number (A000032)

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

31 is a Mersenne prime (A000043, A000668)

32 is the smallest non-trivial 5^th power (A000584)

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

34 is the smallest number with the property that it and its neighbors have the same number of divisors (A169834, A005238)

35 is the number of hexominoes (A000105)

36 is the smallest non-trivial number which is both square (A000290) and triangular (A000217) (I.e. is in A001110)

37 is the maximum number of 5^th powers needed to sum to any number. It is also the third (and probably the last) prime of the form 4k+1, for which all sums Sum_{j=1..u} L(j/p) (with u ranging from 1 to (p-1)/2) are nonnegative, where L(j/p) is Legendre symbol of j and p. (A080114)

38 is the last Roman numeral when written lexicographically

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 a value of n so that x² + x + n takes on prime values for x = 0, 1, 2, ... n-2

42 is the 5^th Catalan number (A000108), and the last one which is an integral multiple of the immediately preceding Catalan number (C₄ = 14). It is also the 3^rd primary pseudoperfect number (A054377).

43 is the number of sided 7-iamonds

44 is the number of derangements of 5 items (A000166)

45 is a Kaprekar number (A006886)

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 of 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 6^th Motzkin number

52 is the 5^th Bell number (A000110)

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

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

55 is the largest triangular number (A000217) in the Fibonacci sequence (A000045). It is the tenth term (after the zero) in both sequences, 55 = A000217(10) = A000045(10)

56 is the number of reduced 5×5 Latin squares A000315)

57 = 111 in base 7 (A023000)

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 (A169823).

60 is also the order of the smallest non-cyclic simple group (A001034)

61 is the 3^rd secant number (A000364)

62 is the smallest number that can be written as the sum of of 3 distinct squares in 2 ways

63 is the number of partially ordered sets on 5 elements (A000112)

64 is the smallest number with 7 divisors

65 is the smallest number that becomes square if its reverse is either added to or subtracted 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 appears latest in the decimal expansion of π

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

70 is the smallest weird number

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 dimensions (A001116)

73 is the smallest multi-digit number which is one less than twice its reverse (A169830)

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

75 is the number of orderings of 4 objects with ties allowed (A000670)

76 is an automorphic number

77 is the largest number that cannot be written as a sum of distinct 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 permutable prime

80 is the smallest number n where n and n+1 are both products of 4 or more primes

81 is the square of the sum of its digits

82 is the number of 6-hexes

83 is the number of strongly connected digraphs with 4 vertices

84 is the largest order of a permutation of 14 elements

85 is the largest n for which 1²+2²+3²+ ... +n² = 1+2+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 (A028387)

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 in 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 is the smallest number with the property that its first 3 multiples contain the digit 9

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

99 is a Kaprekar number (A006886)

100 is the smallest square which is also the sum of 4 consecutive non-zero cubes A027603 (Are there others?)

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

105 is the largest number n known with the property that n - 2^k is prime for k>1. Also, as it is the first natural number to have three distinct odd prime factors (105 = 3*5*7), the 105th cyclotomic polynomial ($\Phi _{105}(x)$) is the first one which has a coefficient with absolute value larger than 1 (A013594).

106 is the number of trees with 10 vertices

107 is the exponent of a Mersenne prime (A000043, A000668)

108 is 3 hyperfactorial

108 is also the number of heptominoes (A000105)

109 has a 5^th root that starts 2.555555...

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

111 is the smallest possible magic constant of a 3×3 magic square of distinct primes

112 is the side of the smallest square that can be tiled with distinct integer -sided squares

113 is a permutable prime

114 = 222 in base 7 (A125725)

115 is the number of rooted trees with 8 vertices (A000081)

116 is a 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 where either n or n+1 is divisible by the numbers from 1 to 8

120 is the smallest number to appear 6 times in Pascal's triangle. It is also the third (and probably the last?) number which is both factorial (A000142) and triangular number (A000217)

121 is the only square known of the form 1 + p + 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 10^th Lucas number (A000032)

124 is the smallest 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 = [1] binomial(9,4) (A007318)

127 is a Mersenne prime (A000043, A000668)

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

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

130 is the number of functions from 6 unlabeled points to themselves

131 is a permutable prime

132 is the smallest number which is the sum of all 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 = ₈C ₁ + ₈C ₃ + ₈C ₄

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

139 is the number of unlabeled topologies with 5 elements

140 is a harmonic divisor number

141 is the 6^th central trinomial coefficient

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 (A000290) in the Fibonacci sequence (A000045). It is the twelfth term (after the zero) in both sequences, 144 = A000290(12) = A000045(12)

145 is a factorion

146 = 222 in base 8

147 is the number of sided 6-hexes

148 is the number of perfect graphs with 6 vertices

149 is the smallest number whose square begins with three 2's

150 = 10010110₂ = 2112₄ = 1100₅, each using 2 different digits an equal number of times

151 is a palindromic prime (A002385)

152 has a square composed of the digits 0-4 (A158304)

153 is a narcissistic number (A005188)

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

155 is the sum of the primes between its smallest and largest prime factor (A169802, A055233)

156 is the number of graphs with 6 vertices (A000088)

157 is a number whose square contains the same digits as the square of its successor (A072841 (the defintion was wrong)

158 is the number of planar partitions of 11 (A000219)

159 is the number of isomers 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 in 9 ways

163 is the largest Heegner Number

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

165 is the midpoint of the n^th larger prime and n^th smaller prime, for 1 ≤ n ≤ 6

166 is the number of monotone Boolean functions of 4 variables

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

168 is the size of the smallest non-cyclic simple group which is not an alternating group (A001034)

169 is the 7^th Pell number. Apparently, the largest square (13x13) in A001653.

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

171 has the same number 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 that can be written as the sum of of 4 positive distinct squares in 6 ways

175 = 1¹ + 7² + 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 another cube

179 has a square comprised of the digits 0-4

180 is the total number of degrees in a triangle

181 is a strobogrammatic prime

182 is the number of connected bipartite graphs with 8 vertices

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

184 is a Kaprekar constant in base 3

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

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

187 is the 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 the property 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 largest number that can be written as ab + ac + bc with 0 < a < b < c in a unique way

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

195 is the smallest value of n such that _2nC _n is divisible by n²

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

197 is a Keith number

198 = 11 + 99 + 88

199 is the 11^th Lucas number (A000032)

200 is the smallest number which can not be made prime by changing one of its digits

201 is a Kaprekar constant in base 4

202 has a cube that contains only even digits

203 is the 6^th Bell number (A000110)

204 is the square root of a triangular number

205 = 5 × 41 = 541₆

206 is the smallest number whose English name contains all five vowels exactly once

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

208 is the 10^th 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 digits are the same

213 is the number of perfect 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 the number of digraphs with 4 vertices

219 is the number 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 the number of lattices on 8 unlabeled nodes

223 is the smallest prime p which has more primitive roots below p/2 than above p/2

224 is the Entringer number E(6,3).

225 is an octagonal square number

226 are the first 3 digits of π ²²⁶

227 is the number of connected planar graphs with 8 edges

228 is the number of ways, up to rotation and reflection, of dissecting a regular 11-gon into 9 triangles

229 is the smallest prime that remains prime 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 is the number of ways to stack 12 pennies in a line so that each penny lies on the table or on two pennies

235 is the number of trees with 11 vertices

236 is the number of possible positions in Othello after 2 moves by both players

237 is the smallest number with the property 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 n^th 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 divisors

243 = 3⁵ (A000032)

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

245 is a stella octangula number

246 = ₉C ₂ + ₉C ₄ + ₉C ₆

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

248 is the smallest number n>1 for which the arithmetic , geometric , 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 multi-digit number so that the sum of the squares of its prime factors equals the 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 5^th central binomial coefficient

253 is the smallest non-trivial triangular star number

254 is the smallest multi-digit composite number all of whose proper divisors contain the digit 2

255 = 11111111 in base 2 (A000225)

256 is the smallest non-trivial 8^th power

257 is a Fermat prime

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

259 = 1111 in base 6

260 is the constant of an 8×8 magic square

261 is the number of essentially different ways to dissect a 16-gon into 7 quadrilaterals

262 is the 5^th meandric number and the 9^th open meandric number

263 is the largest known prime whose square is strobogrammatic

264 is the largest known number whose square is undulating

265 is the number of derangements of 6 items (A001116)

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

267 is the number of planar partitions of 12

268 is the smallest number whose product of digits is 6 times 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 4^th tangent 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 28 in which no part occurs only once

276 = 1⁵ + 2⁵ + 3⁵

277 is a Perrin number

278 is the closest integer to 6^π

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

280 is the number of ways 18 people around a round table can shake 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 (A000081)

287 is the sum of consecutive primes in 3 different ways

288 is the smallest non-palindrome non-square 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 representation

291 is the largest number that is not the sum of distinct non-trivial powers

292 is the number of ways to make change for a dollar

293 is the number of ways to stack 20 boxes in a line so that each box lies on the table or on a box next to 2 boxes

294 is the number of planar 2-connected graphs with 7 vertices

295 is a structured deltoidal hexacontahedral number

296 is the number of partitions of 30 into distinct parts

297 is a Kaprekar number (A006886)

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 cut into with 12 cuts

300 is the largest possible score in bowling (A060853)

301 is a 6-hyperperfect number

302 is the number of ways to play the first 3 moves in checkers (A133046)

303 is the number of bipartite graphs with 8 vertices

304 is a primitive semiperfect number

305 is a hexagonal prism number (A005915)

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 the smallest number whose 5^th power contains every digit at least once

310 = 1234 in base 6

311 is a permutable prime

312 = 2222 in base 5

313 is the number of intersections when all the diagonals of a regular dodecagon are drawn

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 (3¹)⁶

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 sets on 6 elements (A000112)

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 binary 10 X 10 matrix

321 is a Delannoy number

322 is the 12^th Lucas number (A000032)

323 is the smallest composite number n that divides the (n+1)^st Fibonacci number

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 elements

327 is the largest number n so that n, 2n, and 3n together contain every digit from 1-9 exactly once

328 concatenated with its successor is square

329 is the number of forests with 10 vertices

330 = ₁₁C ₄

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

332 is the number of 2-connected graphs with 7 vertices

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 polynomials over GF(2)

336 = ₈P ₃

337 is the number of different resistances that can be created in a circuit of 8 equal resistors

338 is the smallest number for which both the number of divisors and the sum of its prime factors is a perfect number

339 is the number of ways to divide 5 black and 5 white beads into piles

340 is a value of n for which n! + 1 is prime

341 is the smallest pseudoprime in base 2

342 is the number of inequivalent binary linear codes of length 8

343 is a strong Friedman number

344 is the smallest number that can be written as the sum of a cube and a 7^th power in more than one way

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 whose 5^th power contains exactly the same digits as another 5^th power

349 is a Tetranacci -like number starting from 1, 1, 1, and 1

350 is the Stirling number of the second kind 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 4^th power can be written as the sum of four 4^th powers

354 is the sum of the first four 4^th powers

355 is the number of labeled topologies with 4 elements

356 is the smallest happy number of height 6

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 base 7 representation

360 is the number of degrees in a circle.

360 is also the order of a non-cyclic simple group (A001034)

361 is the number of intersections on a Go board (A000290)

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

363 is a perfect totient number

364 = ₁₄C ₃

365 is the smallest number that can be written as a sum of consecutive squares in more than 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 with the pentominoes

369 is the number of octominoes (A000105)

370 is a narcissistic number

371 is a narcissistic number

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 14^th Fibonacci number (A000045)

378 is the maximum number of regions a cube can be cut 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 is the number of necklaces possible with 13 beads, each being one of 2 colors

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 11^th roots of unity

387 is the smallest number with sort-then-add persistence of 10

388 is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 6 stamps

389 is the smallest prime so that it and the next 3 primes are all equal to 1 (mod 4)

390 is the number of partitions of 32 into distinct parts

391  ???

392 is a Kaprekar constant in base 5

393 is the 7^th central trinomial coefficient

394 is a Schröder number

395 does not occur in its factorial in base 2

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 is the number of integers with complexity 22

399 is a Lucas-Carmichael number (A006972)

400 = 1111 in base 7 (A023000)

401 is the number of connected planar Eulerian graphs with 9 vertices

402 is the number of graphs with 8 vertices and 9 edges

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

404 is the number of sided 10-hexes with holes

405 is a pentagonal pyramidal number

406 is the number of ways to tile a 3×17 rectangle with 3×1 rectangles

407 is a narcissistic number

408 is the 8^th Pell number

409 is the number of graphs with 8 vertices with clique number 2

410 is the smallest number that can be written as the sum of 2 distinct prime powers in 2 ways

411 is a member of the Fibonacci -type sequence starting with 1 and 4

412 is the number of subsets of {1,2,3,...,11} that have a sum divisible by 5

413 is a structured hexagonal diamond number

414 is a value of n for which n⁴, n⁵, n⁶, and n⁷ have the same digit sum

415 is the 10^th Iccanobif number, where each term is the reverse of the sum of the previous two numbers

416 is the number of subsets of the 15^th roots of unity that add to a real number

417 is the smallest number so that it and the next 3 numbers have different numbers of distinct prime factors

418 has the property that the sum of its prime factors is equal to the product of its digits

419 is the number of ways to divide a 6×6 grid of points into two sets using a straight line

420 is the smallest number divisible by 1 through 7 (A169825)

421 is the number of commutative monoids of order 6

422 is the smallest number whose 8^th power has 21 digits

423 is a number that does not have any digits in common with its cube

424  ???

425 is the number of subsets of {1,2,3,...,11} that have an integer average

426 is a stella octangula number

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

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

429 is the 7^th Catalan number

430 is the number of necklaces possible with 6 beads, each being one of 4 colors

431 is the index of a prime Fibonacci number

432 = 4 × 3³ × 2²

433 is the index of a prime Fibonacci number

434 is the smallest composite value of n for which σ (n) + 2 = σ (n+2)

435 is the number of ordered partitions of 16 into distinct parts

436 is the smallest number whose cube contains four 8's

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 smallest prime where inserting the same digit between every pair of digits never yields another prime

440 is the number of permutations of 12 items that fix 9 elements

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

442 is the number of planar partitions of 13

443 is a value of n for which σ (n) is a repdigit

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

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 formed 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 of 13-iamonds with holes

451 is the smallest number whose reciprocal has period 10

452 is the closest integer to 7^π

453 is the only number n so that n, 2n, and 6n together contain every digit exactly once

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

455 = ₁₅C ₃

456 is the number of tournaments with 7 vertices

457 is the index of a prime Euclid number

458 is a number that does not have any digits in common with its cube

459 is the smallest number n for which reverse(n) - n contains the same digits as n

460  ???

461 is the number of ways to stack 18 pennies in contiguous rows so that each penny lies on the table or on two pennies

462 = ₁₁C ₅

463 is the smallest prime so that it and the next 6 primes are all equal to 3 (mod 4)

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 has strictly increasing digits in bases 7, 9, and 10

468 = 3333 in base 5

469 is a value of n for 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 digit 4

472 is the number of ways to tile a 5×5 square with integer -sided squares

473 is the largest known number whose square and 4^th power use different digits

474 is a member of the Fibonacci -type sequence starting with 1 and 8

475 has a square that is composed of overlapping squares of smaller numbers

476 is the number of different products of subsets of the set {1, 2, 3, ... 11}

477 is the smallest number whose cube contains four 3's

478 is the 7^th 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 of 2 squares in 8 ways

481 is the number of conjugacy classes in the automorphism group of the 10 dimensional hypercube .

482 is a number whose square and cube use different digits

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

484 is a palindrome in base 3 and in base 10

485 is the number of categories with 6 morphisms and 2 objects

486 is a Perrin number

487 is the number of Hadamard matrices of order 28

488  ???

489 is an octahedral number

490 is the number of partitions of 19

491 is the smallest number n so that the largest prime factors of the numbers n through n+4 decrease

492 is a Hexanacci number

493 is a Lucas 7-step number

494 is the number of unlabeled distributive lattices with 14 elements

495 is the Kaprekar constant for 3-digit numbers

496 is the 3^rd perfect number (A000396)

497 is the number of graphs with 8 edges

498 is the number of necklaces possible with 8 beads, each being one of 3 colors

499 is the number of ways to place 26 points on a 13×13 grid so that no 3 points are on a line

500 is the number of planar partitions 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 primes

504 = ₉P ₃

505 = ₁₀C ₅ + ₁₀C ₀ + ₁₀C ₅

506 is the sum of the first 11 squares

507 is the number of rooted ternary trees with 10 vertices

508  ???

509 is the index of a prime Fibonacci number

510 is the number of binary rooted trees with 14 vertices

511 = 111111111 in base 2 (A000225)

512 is the cube of the sum of its digits

513 is the number of conjugacy classes of the alternating group A₂₂

514  ???

515 is the number of graphs on 6 vertices with no isolated vertices

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

517 does not occur in its factorial in base 2

518 = 5¹ + 1² + 8³

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

520 is the number of ways to place 2 non-attacking kings on a 6×6 chessboard

521 is the 13^th Lucas number (A000032)

522 is the number of ways to place a non-attacking white and black pawn on a 6×6 chessboard

523 is the smallest prime that is followed by 17 composite numbers

524 is the number of 6-kings

525 is a hexagonal pyramidal number

526 is the number of ways to cut a 8×8 chessboard into 2 pieces with equal areas with a cut that only travels up and right

527 is the smallest number n for which there do not exist 4 smaller numbers so that a₁! a₂! a₃! a₄! n! is square

528 concatenated with its successor is square

529 is the smallest number n so that the continued fraction for n/k contains no 2's for any 1 ≤ k ≤ n

530 is the sum of the first 3 perfect numbers (A092336)

531 is the smallest number with the property that its first 4 multiples contain the digit 1

532 is a hendecagonal pyramidal number

533 is the number of degree sequences for graphs with 5 vertices

534  ???

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

536 is the number of solutions of the stomachion puzzle

537 divides the sum of the cubes of the first 537 primes

538 is the 10^th open meandric number

539 is the number of multigraphs with 5 vertices and 9 edges

540 is divisible by its reverse (A169824)

541 is the number of orderings of 5 objects with ties allowed (A000670)

542 is a member of the Fibonacci -type sequence starting with 3 and 8

543 is a number whose square and cube use different digits

544 is the generalized Catalan number C(14,3)

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

546 undulates in bases 3, 4, and 5

547 is the smallest number that can not be written using 11 copies of 11 and the operations +, –, ×, and ÷

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

549  ???

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

553 is a Huay rhombic dodecahedral number

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

555 is a repdigit

556 are the first 3 digits of 4⁵⁵⁶

557  ???

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

559 is a centered cube number

560 = ₁₆C ₃

561 is the smallest Carmichael number

562 is the maximum number of regions a circle can be cut into by joining 11 points on the circumference with straight lines

563 is the largest known Wilson prime

564 is the number of 13-ominoes with a horizontal or vertical line of symmetry

565 is a structured truncated octahedral number

566 is the number of ways to place 24 points on a 12×12 grid so that no 3 points are on a line

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

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

569 is the smallest number n for which the concatenation of n, (n+1), ... (n+30) is prime

570 is the product of 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 bases 2 and 3

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

574 is the maximum 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

577 is a Proth prime

578 is the number of graphs with 7 vertices with clique number 3

579 is the number of graphs with 7 vertices that have chromatic number 3

580 is the 6^th central quadrinomial coefficient

581 has a base 3 representation that begins with its base 4 representation

582 is the number of antisymmetric relations on a 5 element set

583 is the smallest number whose reciprocal has period 26

584 is the number of ways to color the vertices of a triangle with 12 colors, up to rotation

585 is a palindrome in base 2, base 8, and in base 10

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

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

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

589 is a centered tetrahedral number

590 is a value of n for which φ (n) + φ (n+1) divides σ (n) + σ (n+1)

591 is the number of ways to stack 23 boxes in a line so that each box lies on the table or on a box next to 2 boxes

592 evenly divides the sum of its rotations

593 is a Leyland number

594 = 1⁵ + 2⁹ + 3⁴

595 is the number of ways to tile a 3×18 rectangle with 3×1 rectangles

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

597 is a value of n for which n!!! + 1 is prime

598 = 5¹ + 9² + 8³

599 is the smallest number whose digits add to 23

600 and its reverse are both the averages of twin primes

601 is the location of the first occurrence of 3 consecutive zeroes in the decimal digits of π

602 are the first 3 digits of 5⁶⁰²

603 is the smallest number n so that n, n+1, and n+2 are all the product of a prime and the square of a prime

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

605 has a sum of digits equal to its largest prime factor

606 is the first non-trivial number that is both 11-gonal and centered 11-gonal

607 is the exponent of a Mersenne prime (A000043, A000668)

608 is a number that does not have any digits in common with its cube

609 is a strobogrammatic number

610 is the smallest Fibonacci number that begins with 6

611  ???

612 is a number whose square and cube use different digits

613 is the index of a prime Lucas number

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

615 is the trinomial coefficient T(10,6)

616 is a Padovan number

617 = 1!² + 2!² + 3!² + 4!²

618 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 to 9-color the faces of a tetrahedron

622  ???

623 is the number of inequivalent asymmetric Ferrers graphs with 23 points

624 is the smallest number with the property that its first 5 multiples contain the digit 2

625 is an automorphic number

626 is a palindrome in base 5 and in base 10

627 is the number of partitions of 20

628 is the sum of the squares of 4 consecutive primes

629 evenly divides the sum of its rotations

630 is a triangular number , 3 times a triangular number , and 6 times a triangular number

631 has a base 2 representation that begins with its base 5 representation

632 is the number of triangles formed by connecting the diagonals of a regular octagon

633 is the smallest number n whose 5^th root has a decimal part that begins with the digits of n

634 is a number n whose 5^th root has a decimal part that begins with the digits of n

635 is a number n whose 5^th root has a decimal part that begins with the digits of n

636 is a number n whose 5^th root has a decimal part that begins with the digits of n

637 = 777 in base 9

638 is the number of fixed 5-kings

639 is a number n whose 5^th root has a decimal part that begins with the digits of n

640 = 16!!!!!!

641 is the smallest prime factor of 2²⁵+1

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

647  ???

648 is the smallest number whose decimal part of its 6^th root begins with the digits 1-9 in some order

649  ???

650 is the sum of the first 12 squares

651 has a 4^th power that is the sum of four 4^th powers

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

654 has a square that is the sum of a cube and 5^th power

655  ???

656 is a palindrome in base 3 and in base 10

657 is the number of ways to tile a 4×22 rectangle with 4×1 rectangles

658 is the number of triangles of any size contained in the triangle of side 13 on a triangular grid

659 is an Eisenstein-Mersenne prime (A066408)

660 is the order of a non-cyclic simple group

661 is the largest prime factor of 8! + 1

662 is the index of the smallest triangular number that contains the digits 1, 2, 3, 4, and 5

663 is the generalized Catalan number C(15,3)

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

665 is a member of the Fibonacci -type sequence starting with 1 and 4

666 is the largest rep-digit triangular number

667 is the number of asymmetric trees with 16 vertices

668 is the number of legal pawn moves in Chess

669 is the number of unsymmetrical ways to dissect a regular 12-gon into 10 triangles

670 is an octahedral number

671 is a rhombic dodecahedral number

672 is a multi-perfect number

673 is a Tetranacci -like number starting from 1, 1, 1, and 1

674  ???

675 is the smallest order for which there are 17 groups

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

677 is the closest integer to 11^e

678 is a member of the Fibonacci -type sequence starting with 1 and 7

679 is the smallest number with multiplicative persistence 5

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

681 divides the sum of the first 681 composite numbers

682 = ₁₁C ₆ + ₁₁C ₈ + ₁₁C ₂

683 is a Wagstaff prime

684 is the sum of 3 consecutive cubes

685  ???

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

687 is the closest integer to 8^π

688 is a Friedman number

689 is the smallest number that can be written as the sum of 3 distinct squares in 9 ways

690 is the smallest number that can not be written as the sum of a triangular number , a cube , and a Fibonacci number

691 is the smallest prime p for which x⁵ = x⁴ + x³ + x² + x + 1 (mod p) has 5 solutions

692 is a number that does not have any digits in common with its cube

693 are the first 3 decimal digits of ln (2)

694 is the number of different arrangements (up to rotation and reflection) of 7 non-attacking rooks on a 7×7 chessboard

695 is the maximum number of pieces a torus can be cut into with 15 cuts

696 is a palindrome n so that n(n+8) is also palindromic

697 is a 12-hyperperfect number

698 = 3² + 4³ + 5⁴

699 is a value of n for which |cos(n)| is smaller than any previous integer

700 is the number of symmetric 8-cubes

701 = 1⁰ + 2¹ + 3² + 4³ + 5⁴

702  ???

703 is a Kaprekar number (A006886)

704 is the number of sided octominoes

705 is the smallest Lucas pseudoprime

706  ???

707 is the smallest number whose reciprocal has period 12

708 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps

709 is the number of connected planar graphs with 9 edges

710 is the number of connected graphs with 9 edges

711 is the name of a chain of convenience stores

712 is the largest number known that does not have any digits in common with its 8^th power

713 is the number of commutative monoids of order 7 with 4 idempotents

714 is the smallest number which has equal numbers of every digit in bases 2 and 5

715 = ₁₃C ₄

716 is the smallest number whose cube contains four 6's

717 is a palindrome in base 2 and in base 10

718 is the number of unlabeled topologies with 6 elements

719 is the number of rooted trees with 10 vertices (A000081)

720 = 6!

721 is the smallest number which can be written as the difference of 2 cubes in 2 ways

722 is the sum of the 4^th powers of the first 3 primes

723 = (1!)! + (2!)! + (3!)!

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

725  ???

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

737 is a Boeing plane

738 = 6 + 66 + 666

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

745 is the smallest number whose square begins with three 5's

746 = 1⁷ + 2⁴ + 3⁶

747 is a Boeing plane

748 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner

749 is the number of ways to divide a 7×7 grid of points into two sets using a straight line

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 .

753 is the smallest number whose cube contains 4 consecutive 7's

754  ???

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

758  ???

759 is the number of octads in the large Witt design

760 is the number of partitions of 37 into distinct parts

761  ???

762 is the starting location of 999999 in the decimal expansion of π

763 is the smallest number whose 4^th power contains every digit at least once

764 is the number of 8×8 symmetric permutation matrices

765 is a Kaprekar constant in base 2

766 is the number of series-reduced planted trees with 9 leaves

767 is the largest n so that n² = _mC ₀ + _mC ₁ + _mC ₂ + _mC ₃ has a solution

768 is the number of subsets of {1,2,3,...,12} that have an integer average

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

770 is the number of digits of the 15^th perfect number (A061193)

771 is the number of intersections when all the diagonals of a regular 14-gon are drawn

772  ???

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

774  ???

775 is the smallest number whose 9^th power has 26 digits

776  ???

777 is a repdigit in base 6 and in base 10

778 is the number of ways a 5×1 rectangle can be surrounded by 5×1 rectangles

779  ???

780 = (5+7) × (5+8) × (5+0)

781 = 11111 in base 5

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

783 is the number of 11-ominoes that tile the plane by translation

784 is the sum of the first 7 cubes

785 are the last 3 digits of the sum of the first 785 squares

786 is the largest known n for which _2nC _n is not divisible by the square of an odd prime

787 is a palindrome in base 3 and in base 10

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

789 are the first 3 digits of 9⁷⁸⁹

790  ???

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 = 1⁶ + 2⁶ + 3⁶

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

796  ???

797 is the number of functional graphs on 9 vertices

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

799 is the smallest number whose sum of digits is composite and whose sum of digits cubed is prime

800 = 2222 in base 7 (A125725)

801 = (7! + 8! + 9! + 10!) / (7 × 8 × 9 × 10)

802 is the number of isomers of C₁₃H₂₈

803 is a value of n for which σ (n) is a repdigit

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

805 is the number of possible positions in Checkers after 4 moves

806 is not the sum of a square , a cube , a 4^th power, and a 5^th power

807  ???

808 is a strobogrammatic number

809 is a member of the Fibonacci -type sequence starting with 1 and 5

810 is a value of n for which n-1 and n+1 are twin primes , and so are 2n-1 and 2n+1

811  ???

812 is the number of triangles of any size contained in the triangle of side 14 on a triangular grid

813 are the first 3 digits of 813^e

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

815 is a Lucas 3-step number

816 = ₁₈C ₃

817  ???

818 is the number of ways to dissect a 12-gon using non-crossing diagonals into polygons with an even number of sides.

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

823 is a number that does not have any digits in common with its cube

824  ???

825 is the number of ways to legally add 2 sets of parentheses to a product of 9 variables

826  ???

827 is the number of asymmetric trees with 11 vertices

828  ???

829 is a value of n for which π(n) is the product of the digits of n

830  ???

831 is the number of monic polynomials of degree 9 with integer coefficients whose complex roots are all in the unit disk

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

833 is a centered octahedral number

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

835 is the 9^th Motzkin number

836 is a non-palindrome with a palindromic square

837  ???

838  ???

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 the ratio of Fibonacci numbers

843 is the 14^th Lucas number (A000032)

844 is the smallest number so that it and the next four numbers are squareful numbers

845  ???

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

847 is the sum of the digits of the 14^th Mersenne prime (A066538)

848 is the number of inequivalent binary linear codes of length 9

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

851 is the number of ordered partitions of 18 into distinct parts

852 is the number of 6-colorable connected graphs with 7 vertices

853 is the number of connected graphs with 7 vertices (A001349)

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

856 is a member of the Fibonacci -type sequence starting with 1 and 9

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 (A000219)

860  ???

861 = 7 + 77 + 777

862 is a number whose sum of divisors is a 4^th 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 (A000009)

865  ???

866 is the number of sided 10-iamonds (A006534)

867 is the number of graphs with 8 vertices that have chromatic number 5

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

869 is the number of different resistances that can be created in a circuit of 9 equal resistors (A048211)

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

871  ???

872 is a value of n for which n! + 1 is prime (A002981)

873 = 1! + 2! + 3! + 4! + 5! + 6! (A007489)

874 is the number of positive integer solutions to (1 + 1/a)(1 + 1/b)(1 + 1/c)(1 + 1/d)(1 + 1/e) = 2

875 is 3-automorphic

876 is a dodecagonal pyramidal number (A007587)

877 is the 7^th Bell number (A000110)

878 is the number of 3×3 sliding puzzle positions that require exactly 29 moves to solve starting with the hole on a side

879 is a number n whose 5^th root has a decimal part that begins with the digits of n

880 is the number of 4×4 magic squares (A006052)

881 is a number n whose 5^th root has a decimal part that begins with the digits of n

882 is the smallest number whose square begins with three 7's

883 is a number n whose 5^th root has a decimal part that begins with the digits of n

884 is a number n whose 5^th root has a decimal part that begins with the digits of n

885 is an enneagonal pyramidal number (A007584)

886  ???

887 is a value of n for which σ (n) is a repdigit

888 and the following 18 numbers are composite

889 is a Kaprekar constant in base 2

890  ???

891 is the number of unlabeled distributive lattices with 15 elements

892 is the smallest integer ratio of a 13-digit number to its product of digits

893 has a square whose digits each occur twice

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

895 is a Woodall number (A003261)

896 is not the sum of 4 non-zero squares

897 is a Cullen number (A002064)

898 is a member of the Fibonacci -type sequence starting with 2 and 5

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

903 is the 6^th super Catalan number

904 has a cube that is the sum of 3 positive cubes

905 is the smallest composite number that is not the sum of a prime and a power of 2

906 is the number of perfect graphs with 7 vertices

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

908  ???

909 is a value of n that has has no digits in common with 2n, 3n, 4n, 5n, 6n, 7n, 8n, or 9n

910 is the generalized Catalan number C(11,4)

911 is the American emergency number

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

915  ???

916 is a strobogrammatic number

917 is the only positive number known whose 9^th power can be written as the sum of ten 9^th powers

918 is a number that does not have any digits in common with its cube

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

920 is a truncated cube number

921  ???

922 = 1234 in base 9

923 multiplied by its successor gives a number concatenated with itself

924 is the 6^th central binomial coefficient

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

926 is the smallest number that can not be formed using the digits 1-6 at most once, with the operators +, –, ×, ÷, and ^

927 is the 13^th tribonacci number

928  ???

929 is a Proth prime

930 is the number of even permutations on 7 elements with no fixed points

931  ???

932  ???

933 is a house number

934 has a 5^th root that starts 3.25252225...

935 is a Lucas-Carmichael number (A006972)

936 is a pentagonal pyramidal number

937  ???

938  ???

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

942 is the smallest number whose cube contains five 8's

943 is a Lucas 6-step number

944  ???

945 is the smallest odd abundant number (A005101, A005231)

946 is a hexagonal pyramidal number

947  ???

948 is the number of symmetric plane partitions of 24

949 is the larger number in a Ruth-Aaron pair

950 is the generalized Catalan number C(17,3)

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

954  ???

955 is the number of ways to to arrange the numbers 1-9 around a circle so that the sums of adjacent numbers are distinct

956 is the number of multigraphs with 16 vertices and 4 edges

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

958 is the number of labeled 3-colorable graphs with 5 vertices

959 is a Carol number (A093112)

960 is the sum of its digits and the cube of its digits (A065138)

961 is a square whose digits can be rotated to give another square (A035126)

962  ???

963 is a value of n for which π(n) is the product of the digits of n (A097220)

964 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in the center (A089474)

965  ???

966 is the Stirling number of the second kind S(8,3) (A008277, A048993, A000392)

967 is the number of 6-digit triangular numbers (A068094)

968 is an Achilles number (A052486)

969 is a tetrahedral palindrome (A006030)

970  ???

971  ???

972 is an Achilles number (A052486)

973 is the number of inequivalent asymmetric Ferrers graphs with 25 points (A000701)

974 is the number of multigraphs with 5 vertices and 10 edges (A014395)

975 is the number of 11-ominoes that contain 1 hole (A057418)

976 has a square formed by inserting a block of digits inside itself (A052212)

977 is a Stern prime (A042978)

978 2⁴ + 3⁴ + 4⁴ + 5⁴

979 is the sum of the first five 4^th powers (A000538)

980  ???

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 (A000009)

983 is a Wedderburn-Etherington number (A001190)

984 = 8 + 88 + 888 (A099675)

985 is the 9^th Pell number (A000129)

986 is a strobogrammatic number (A000787)

987 is the 16^th Fibonacci number (A000045)

988 is the maximum number of regions a cube can be cut into with 18 cuts (A000125)

989 is the smallest number such that it and its reverse are divisible by 43 (A055483)

990 is a triangular number that is the product of 3 consecutive integers (A001219)

991 is a permutable prime (A003459, A129338)

992 is the number of differential structures on the 11-dimensional hypersphere (A001676)

993 is the number of paraffins with 8 carbon atoms (A005961)

994 is the smallest number with the property that its first 18 multiples contain the digit 9 (A039940)

995 has a square formed by inserting a block of digits inside itself (A046829)

996 has a square formed by inserting a block of digits inside itself (A046829)

997 has a cube root that starts 9.98998998...

998 is the smallest number with the property that its first 55 multiples contain the digit 9 (A039940)

999 is a Kaprekar number (A006886)