# Điều bí ẩn của những con số

Được đăng bởi tonami, Feb 27 2005 07:08 AM

14 trả lời cho chủ đề này

### #1

Đăng vào: 27 February 2005 - 07:08 AM

Điều bí ẩn của những con số

Đây là một trang web rất hay nói về bí ẩn của những con số từ 1 đến 9999.

Bạn nào giỏi toán bằng tiếng Anh xin dịch giúp Ami ạ.

Đây là một trang web rất hay nói về bí ẩn của những con số từ 1 đến 9999.

Bạn nào giỏi toán bằng tiếng Anh xin dịch giúp Ami ạ.

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### #2

Đăng vào: 27 February 2005 - 07:09 AM

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 integer-sided

rectangles that tile a rectangle so that no 2 rectangles share a common length.

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

Archimedian solids.

14 is the smallest number n with the

property that there are no numbers

relatively prime

to n smaller numbers.

15 is the smallest

composite number

n with the property that there is only one

group of order n.

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 that is twice the

sum of its digits.

19 is the maximum number of 4^{th}

powers needed to sum to any number.

20 is the number of

rooted trees with 6

vertices.

21 is the smallest number of distinct

squares needed to tile a

squares.

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 than its

square root.

25 is the smallest

square that can be

written as a sum of 2

squares.

26 is the only 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.

29 is the 7^{th}

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 5^{th} power

(besides 1).

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.

35 is the number of

hexominoes.

36 is the smallest number (besides 1)

which is both square

and triangular.

37 is the maximum number of 5^{th}

powers needed to sum to any number.

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 the smallest number that is not of

the form |2^{x} - 3^{y}|.

42 is the 5^{th}

Catalan number.

43 is the number of sided

7-iamonds.

44 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 9x9 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.

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

in the Fibonacci

sequence.

56 is the number of reduced 5 x 5

Latin squares.

57 = 111 in base 7.

58 is the number of

commutative

semigroups of order 4.

59 is the smallest number whose 4^{th}

power is of the form a^{4}+b^{4}-c^{4}.

60 is the smallest number divisible by 1

through 6.

61 is the 6^{th}

Euler number.

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 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 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 last 2-digit string to appear

in the decimal expansion of .

69 has the property that n^{2}

and n^{3} together contain each digit once.

70 is the smallest

abundant number

that is not the sum of some 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 dimensions.

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 number 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 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

zero-less

pandigital squares.

84 is the largest order of a

permutation of 14

elements.

85 is the largest n for which 1^{2}+2^{2}+1^{2}+...+n^{2}

= 1+2+1+...+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 = 8^{1} + 9^{2}

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 8x8 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.

100 is the smallest

square which is

also the sum of 4 consecutive

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.

105 is the largest number n known with

the property that n - 2^{k} 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 in

bases 5 and 9.

110 is the smallest number that is the

product of two different substrings.

111 is the smallest possible magic

constant of a 3 x 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.

115 is the number of

rooted trees with 8

vertices.

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.

121 is the only

square known of the

form 1+p+p^{2}+p^{3}+p^{4}, 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.

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 = _{9}C_{4}.

127 is a

Mersenne prime.

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

phi(n).

134 = _{8}C_{1} + _{8}C_{3}

+ _{8}C_{4}.

135 = 1^{1} + 3^{2} + 5^{3}.

136 is the sum of the

cubes of the digits

of the sum of the cubes

of its digits.

137 is the maximum number of 7^{th}

powers that are needed to sum to any arbitrarily large number.

138 is the smallest possible product of

3 primes, one of

which is the concatenation of the other two.

139 is the number of unlabeled

topologies with

5 elements.

140 is the smallest

harmonic

divisor number.

141 is a

Cullen number.

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 sequence.

145 = 1! + 4! + 5!

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 concatenation of the first 3

positive squares

150 is the smallest n for which n + n

times the n^{th}

prime is square.

151 is a

palindromic prime.

152 ???

153 = 1^{3} + 5^{3} + 3^{3}.

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.

156 is the number of

graphs with 6 vertices.

157 is the largest number known whose

square contains the

same digits as its successor.

158 is the number of

planar partitions

of 11.

159 is the number of isomers of C_{11}H_{24}.

160 is the number of

9-iamonds.

161 is a

hexagonal

pyramidal number.

162 ???

163 is the largest

Heegner Number.

164 ???

165 = _{11}C_{3}.

166 is the number of monotone

Boolean functions

of 4 variables.

167 ???

168 is the size of the smallest non-cyclic

simple group which

is not an

alternating group.

169 is a

square whose digits

are non-decreasing.

170 is the smallest number n for which

phi(n) and

sigma(n) are

both square.

171 is a

palindromic

triangular number.

172 = 444 in base 6.

173 ???

174 ???

175 = 1^{1} + 7^{2} + 5^{3}.

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 ???

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 ???

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 ditinct

prime factors are

palindromic in

Roman numerals.

191 is a

palindromic prime.

192 is the smallest number with 14

divisors.

193 ???

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_{2n}C_{n} is divisible by n^{2}.

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.

200 is the smallest number which can not

be made prime by

changing one of its digits.

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### #3

Đăng vào: 27 February 2005 - 07:17 AM

201 is a

Kaprekar constant

in base 4.

202 ???

203 is the 6^{th}

Bell number.

204 ???

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 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 ???

209 is the smallest quasi-Carmichael

number in base 9.

210 is the product of the first 4

primes.

211 ???

212 has a

square with 4/5 of

the digits are the same.

213 ???

214 ???

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 10 unlabeled

nodes.

223 is the smallest

prime which will nor

remain prime if one

of its digits is changed.

224 ???

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

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 7x7

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 ???

237 is the smallest number with the

property that its first 3 multiples contain the digit 7.

238 ???

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 ???

242 is the smallest number n where n

through n+1 are all products of 3 or more

primes.

243 = 3^{5}.

244 is the smallest number (besides 2)

that can be written as the sum of 2

squares or the sum

of 2 5^{th} powers.

245 is a

stella

octangula number.

246 = _{9}C_{2} + _{9}C_{4}

+ _{9}C_{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 phi(n)

and sigma(n) are

all integers.

249 ???

250 ???

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

composite number

all of whose divisors (except 1) contain the digit 2.

255 = 11111111 in base 2.

256 is the smallest 8^{th} power

(besides 1).

257 is a

Fermat prime.

258 ???

259 = 1111 in base 6.

260 ???

261 is the number of essentially different

ways to dissect a 16-gon

into 7 quadrilaterals.

262 is the 9^{th} 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.

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 ???

270 is a

harmonic

divisor number.

271 ???

272 is the 7^{th}

Euler number.

273 = 333 in base 9.

274 is the

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

275 ???

276 is the sum of the first 3 5^{th}

powers.

277 ???

278 ???

279 is the smallest number whose product

of digits is 7 times the sum of its digits.

280 ???

281 ???

282 is the sum of its

proper divisors

that contain the digit 4.

283 = 2^{5} + 8 + 3^{5}.

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 ???

288 is the smallest non-palindrome

that when multiplied by its reverse is a

square.

289 is a

square whose digits

are non-decreasing.

290 ???

291 is the number of

functional graphs

on 8 vertices.

292 is the number of ways to make change

for a dollar.

293 ???

294 ???

295 ???

296 ???

297 is a

Kaprekar number.

298 ???

299 ???

300 ???

301 is a

6-hyperperfect

number.

302 is the number of

acyclic digraphs

with 5 vertices.

303 has a

cube that is a

concatenation of other

cubes.

307 is a non-palindrome

with a palindromic

square.

308 is a

heptagonal

pyramidal number.

311 is a permutable

prime.

312 = 2222 in base 5.

313 is a

palindromic prime.

315 = (4+1)(4+1)(4+5).

318 is the number of unlabeled

partially

ordered sets of 6 elements.

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

x 10 matrix of 0's and 1's.

322 is the 12^{th}

Lucas number.

323 is the product of

twin primes.

325 is a

3-hyperperfect

number.

327 and its double and triple together

contain every digit from 1-9 exactly once.

330 = _{11}C_{4}.

333 is the number of

7-hexes.

335 is the number of degree 12

irreducible

polynomials over GF(2).

336 = _{8}P_{3}.

337 is a permutable

prime.

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

prime.

341 is the smallest

pseudoprime in base

2.

342 = 666 in base 7.

343 = (3+4)^{3}.

344 is an

octahedral number.

345 is half again as large as the sum of

its proper divisors.

350 is the

Stirling number of the second kind S(7,4).

351 is the smallest number n where n,

n+1, and n+2 are all products of 4 or more

primes.

352 is the number of different arrangements

of 9 non-attacking queens on an 9x9 chessboard.

353 is the smallest number whose 4^{th}

power can be written as the sum of 4 4^{th} powers.

354 is the sum of the first 4 4^{th}

powers.

355 is the number of labeled

topologies with

4 elements.

360 is the number of degrees in a circle.

364 = _{14}C_{3}.

365 is the smallest number that can be

written as a sum of consecutive

squares in more

than 1 way.

367 is the largest number whose

square has strictly

increasing digits.

369 is the number of

octominoes.

370 = 3^{3} + 7^{3} + 0^{3}.

371 = 3^{3} + 7^{3} + 1^{3}.

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.

381 is a

Kaprekar constant

in base 2.

383 is the number of

Hamiltonian graphs

with 7 vertices.

384 = 8!!.

385 is the number of

partitions of 18.

392 is a

Kaprekar constant

in base 5.

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

prime.

400 = 1111 in base 7.

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### #4

Đăng vào: 27 February 2005 - 07:18 AM

401 is the number of

connected

planar

Eulerian graphs

with 9 vertices.

405 is a

pentagonal

pyramidal number.

407 = 4^{3} + 0^{3} + 7^{3}.

410 is the smallest number that can

written as the sum of 2 distinct

primes in 2 ways.

420 is the smallest number divisible by 1

through 7.

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.

432 = (4) (3)^{3} (2)^{2}.

438 = 666 in base 8.

441 is the smallest

square which is the

sum of 6 consecutive

cubes.

442 is the number of

planar partitions

of 13.

444 is the largest known n for which there

is a unique integer solution to a_{1}+...+a_{n}=(a_{1})...(a_{n}).

446 is the smallest number that can be

written as the sum of 3 distinct

squares in 8 ways.

448 is the number of

10-iamonds.

450 = (5+4)(5+5)(5+0).

454 is the largest number known that

cannot be written as a sum of 7 or fewer

cubes.

455 = _{15}C_{3}.

456 is the number of

tournaments with 7

vertices.

461 = 444 + 6 + 11.

462 = _{11}C_{5}.

465 is a

Kaprekar constant

in base 2.

468 = 3333 in base 5.

469 is the largest known value of n for

which n!-1 is prime.

471 is the smallest number with the

property that its first 4 multiples contain the digit 4.

480 is the smallest number which can be

written as the difference of 2

squares in 8 ways.

483 is the last 3-digit string in the

decimal expansion of

.

484 is a

palindromic

square number.

487 is the number of

Hadamard matrices

of order 28.

489 is an

octahedral number.

490 is the number of

partitions of 19.

495 is the

Kaprekar constant

for 3-digit numbers.

496 is the 3^{rd}

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.

501 is the number of

partitions of 5 items

into ordered lists.

503 is the smallest

prime which is the

sum of the cubes of

the first few primes.

504 = _{9}P_{3}.

505 = _{10}C_{5} + _{10}C_{0} + _{10}C_{5}.

510 is the number of

binary

rooted trees with 14

vertices.

511 = 111111111 in base 2.

512 is the

cube of the sum of

its digits.

518 = 5^{1} + 1^{2} + 8^{3}.

521 is the 13^{th}

Lucas number.

525 is a

hexagonal

pyramidal number.

527 is the smallest number n for which

there do not exist 4 smaller numbers a_{1} through a_{4} so that

a_{1}! a_{2}! a_{3}! a_{4}! n! is

square.

528 is the sum of its

proper divisors

that contain the digit 6.

531 is the smallest number with the

property that its first 4 multiples contain the digit 1.

538 is the 10^{th} meandric number.

540 is divisible by its reverse.

541 is the number of orderings of 5 objects

with ties allowed.

546 undulates in bases 3, 4, and 5.

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

repdigit.

559 is a

centered cube

number.

560 = _{16}C_{3}.

561 is the smallest

Carmichael number.

563 is the largest known

Wilson prime.

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 7 7^{th} powers.

570 is the product of all the

prime

palindromic

Roman numerals.

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.

575 is a

palindrome

that is one less than a

square.

576 is the number of 4 x 4

Latin squares.

582 is the number of

antisymmetric

relations on a 5 element set.

585 = 1111 in base 8.

586 is the smallest number that appears

in its factorial 6 times.

594 = 1^{5} + 2^{9} + 3^{4}.

595 is a

palindromic

triangular number.

598 = 5^{1} + 9^{2} + 8^{3}.

607 is the exponent of a

Mersenne prime.

610 is the 15^{th}

Fibonacci number.

614 is the smallest number that can be

written as the sum of 3

squares in 9 ways.

619 is a

strobogrammatic

prime.

620 is the number of sided

7-hexes.

624 is the smallest number with the

property that its first 5 multiples contain the digit 2.

625 is an

automorphic number.

627 is the number of

partitions of 20.

630 is the number of degree 13

irreducible

polynomials over GF(2).

637 = 777 in base 9.

641 is the smallest

prime factor of 2^{25}+1.

642 is the smallest number with the

property that its first 6 multiples contain the digit 2.

645 is the largest n for which

1+2+1+...+n = 1^{2}+2^{2}+1^{2}+...+k^{2} for

some k.

646 is the number of

connected

planar graphs with 7

vertices.

650 is the sum of the first 12

squares.

651 is an

nonagonal

pentagonal number.

652 is the only known

non-perfect number

whose number of divisors and sum of smaller divisors are

perfect.

660 is the order of a non-cyclic

simple group.

666 is a

palindromic

triangular number.

670 is an

octahedral number.

671 is a

rhombic

dodecahedral number.

672 is a

multi-perfect

number.

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 = _{11}C_{6} + _{11}C_{8} + _{11}C_{2}.

688 has a factorization using the same

digits as itself.

689 is the smallest number that can be

written as the sum of 3 distinct

squares in 9 ways.

697 is a

12-hyperperfect

number.

703 is a

Kaprekar number.

704 is the number of sided

octominoes.

709 is the number of

connected

planar graphs with 9

edges.

710 is the number of

connected graphs

with 9 edges.

714 is the smallest number which has

equal numbers of every digit in bases 2 and 5.

715 = _{13}C_{4}.

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 10x10 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 = 3^{6}.

730 is the number of

connected

bipartite graphs

with 9 vertices.

731 is the number of

planar partitions

of 14.

732 = 1^{7} + 2^{6} + 3^{5}

+ 4^{4} + 5^{3} + 6^{2} + 7^{1}.

733 = 7 + 3! + (3!)!.

735 is the smallest number that is the

concatenation of its distinct

prime factors.

736 = 7 + 3^{6}.

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.

746 = 1^{7} + 2^{4} + 3^{6}.

750 is the

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

757 is the smallest number whose

reciprocal has a period of 27.

762 is the first decimal digit of

where a digit occurs four times in a row.

764 is the number of 8x8

symmetric

permutation

matrices.

765 is a

Kaprekar constant

in base 2.

767 is the largest n so that n^{2}

= _{m}C_{0} + _{m}C_{1} + _{m}C_{2}

+ _{m}C_{3} has a solution.

777 is a

repdigit in bases 6 and

10.

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

781 = 11111 in base 5.

784 is the sum of the first 7

cubes.

787 is a

palindromic prime.

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 3 6^{th}

powers.

797 is the number of

functional graphs

on 9 vertices.

800 = 2222 in base 7.

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### #5

Đăng vào: 27 February 2005 - 07:20 AM

802 is the number of

isomers of C_{13}H_{28}.

810 is divisible by its reverse.

816 = _{18}C_{3}.

820 = 1111 in base 9.

822 is the number of

planar graphs with 7

vertices.

835 is the 9^{th}

Motzkin number.

836 is a non-palindrome

with a palindromic

square.

840 is the smallest number divisble by 1

through 8.

841 is a

square that is also

the sum of 2 consecutive

squares.

843 is the 14^{th}

Lucas number.

846 has the property that its

square is the

concatenation of two consecutive numbers.

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.

858 is the smallest

palindrome

with 4 different prime

factors.

866 is the number of sided

10-iamonds.

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

prime.

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

877 is the 7^{th}

Bell number.

880 is the number of 4 x 4

magic squares.

888 has a

cube that whose

digits each occur 3 times.

889 is a

Kaprekar constant

in base 2.

891 is an

octahedral number.

895 is a

Woodall number.

899 is the product of

twin primes.

900 is a

square whose digits

are non-increasing.

901 is the sum of the digits of the first

100 positive integers.

906 is the number of

perfect graphs with

7 vertices.

907 is the largest n so that **Q**(n)

has class number 3.

912 has exactly the same digits in 3

different bases.

913 has exactly the same digits in 3

different bases.

914 is the number of

binary

rooted trees with 15

vertices.

919 is a permutable

prime.

924 is the 6^{th}

central

binomial coefficient.

929 is a

palindromic prime.

936 is a

pentagonal

pyramidal number.

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.

951 is the number of functions from 8

unlabeled points to themselves.

952 = 9^{3} + 5^{3} + 2^{3}

+ (9)(5)(2).

961 is a

square whose digits

can be rotated to give another

square.

966 is the

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

969 is a tetrahedral

palindrome.

976 has a

square formed by

inserting a block of digits inside itself.

979 is the sum of the first 5 4^{th}

powers.

981 is the smallest number that has 5

different partitions

into 3 parts with the same product.

986 = 1^{9} + 2^{8} + 3^{6}.

987 is the 16^{th}

Fibonacci number.

990 = _{11}P_{3}.

991 is a permutable

prime.

992 is the number of differential structures

on the 11-dimensional

hypersphere.

993 is the smallest number with the

property that its first 15 multiples contain the digit 9.

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 = 10^{3}.

1001 is the smallest

palindromic

product of 3 consecutive

primes.

1002 is the number of

partitions of 22.

1006 has a

cube that is a

concatenation of other

cubes.

1016 is a

stella

octangula number.

1021 is the largest

prime p known with

the property that 1 + (2)(3)(5)(7)(11)...(p) is

prime.

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.

1031 is the length of the largest

repunit that is known to

be prime.

1033 = 8^{1} + 8^{0} + 8^{3}

+ 8^{3}.

1036 = 4444 in base 6.

1044 is the number of

graphs with 7 vertices.

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.

1067 has exactly the same digits in 3

different bases.

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.

1089 is one ninth of its reverse.

1092 is the order of a non-cyclic

simple group.

1093 is the smallest

Wieferich prime.

1098 = 11 + 0 + 999 + 88.

1099 = 1 + 0 + 999 + 99.

1104 is a

Keith number.

1105 is a

rhombic

dodecahedral number.

1106 is a

truncated

tetrahedral number.

1111 is a

repdigit.

1116 is the number of

polyaboloes with 8

half squares.

1122 = _{33}C_{1} + _{33}C_{1} + _{33}C_{2} + _{33}C_{2}.

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 6^{th}

power can be written as the sum of 7 6^{th} powers.

1148 is the number of ways to fold a strip

of 9 stamps.

1153 is the smallest number with the

property that its first 3 multiples contain the digit 3.

1155 is the product of 4 consecutive

primes.

1156 is a

square whose digits

are non-decreasing.

1161 is the number of degree 14

irreducible

polynomials over GF(2).

1166 is a

heptagonal

pyramidal number.

1167 is the smallest number whose 8^{th}

power can be written as the sum of 9 8^{th} powers.

1170 = 2222 in base 8.

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.

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.

1206 has a factorization using the same

digits as itself.

1210 is an

amicable number.

1215 is the smallest number n where n and

n+1 are both products of 6 or more

primes.

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.

1230 has the property that 1^{7}

+ 2^{7} + 3^{7} + 0^{7} equals 1230 written in base 8.

1231 has the property that 1^{7}

+ 2^{7} + 3^{7} + 1^{7} equals 1230 written in base 8.

1233 = 12^{2} + 33^{2}.

1241 is a

centered cube

number.

1243 is the number of essentially different

ways to dissect a 18-gon into 8

quadrilaterals.

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.

1255 is the number of

partitions of 23.

1260 is the smallest number with 36

divisors.

1276 = 1111 + 22 + 77 + 66.

1278 = 1111 + 2 + 77 + 88.

1279 is the exponent of a

Mersenne prime.

1285 is the number of

9-ominoes.

1287 = _{13}C_{5}.

1294 is the number of 4 dimensional

polytopes with 8

vertices.

1295 = 5555 in base 6.

1296 is the number of

labeled trees with 6

vertices.

1300 is the sum of the first 4 5^{th}

powers.

1301 is the number of

trees with 13 vertices.

1306 = 1^{1} + 3^{2} + 0^{3}

+ 6^{4}.

1320 = _{12}P_{3}.

1330 = _{21}C_{3}.

1331 is a

cube containing only

odd digits.

1364 is the 15^{th}

Lucas number.

1365 = _{15}C_{4}.

1366 = 1 + 33 + 666 + 666.

1368 is the number of ways to fold a 3x3

rectangle of stamps.

1369 is a

square whose digits

are non-decreasing.

1370 = 1^{2} + 37^{2} + 0^{2}.

1371 = 1^{2} + 37^{2} + 1^{2}.

1376 is the smallest number with the

property that it and its neighbors are not

cubefree.

1385 is the 8^{th}

Euler number.

1386 = 1 + 3^{4} + 8 + 6^{4}.

1395 is a

vampire number.

1405 is the sum of consecutive

squares in 2 ways.

1419 is a

Zeisel number.

1429 is the smallest number whose

square has the

first 3 digits the same as the next 3 digits.

1430 is the 8^{th}

Catalan number.

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.

1453 = 1111 + 4 + 5 + 333.

1454 = 11 + 444 + 555 + 444.

1455 is the number of

subgroups of the

symmetric group

on 6 symbols.

1458 is the maximum

determinant of a 11

x 11 matrix of 0's and 1's.

1459 = 11 + 444 + 5 + 999.

1467 has the property that e^{1467}

is within 10^{-8} of an integer.

1469 is an

octahedral number.

1470 is a

pentagonal

pyramidal number.

1476 is the number of

graphs with 9 edges.

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

prime.

1494 is the sum of its

proper divisors

that contain the digit 4.

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

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### #6

Đăng vào: 27 February 2005 - 07:22 AM

1503 has a

factorization using the same digits as itself.

1506 is the sum of its

proper divisors

that contain the digit 5.

1508 is a

heptagonal

pyramidal number.

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.

1533 is a

Kaprekar constant

in base 2.

1537 has its largest

proper divisor as

a substring.

1540 is a

tetrahedal

triangular number.

1543 = 1111 + 55 + 44 + 333.

1547 is a

hexagonal

pyramidal number.

1555 is the largest n so that **Q**(n)

has class number 4.

1562 = 22222 in base 5.

1563 is the smallest number with the

property that its first 4 multiples contain the digit 6.

1575 is the number of

partitions of 24.

1595 is the smallest quasi-Carmichael

number in base 2.

1597 is the 17^{th}

Fibonacci number.

1600 = 4444 in base 7.

1606 is the number of

strongly

connected digraphs with 4 vertices.

1624 is the

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

1632 is the smallest number with the

property that its first 5 multiples contain the digit 6.

1634 = 1^{4} + 6^{4} + 3^{4}

+ 4^{4}.

1638 is a

harmonic

divisor number.

1639 is the number of

binary

rooted trees with 16

vertices.

1640 = 2222 in base 9.

1650 has exactly the same digits in 3

different bases.

1676 = 1^{1} + 6^{2} + 7^{3}

+ 6^{4}.

1680 is the smallest number with 40

divisors.

1681 is a

square and each of

its two 2-digit parts is

square.

1688 is a

truncated

tetrahedral number.

1689 is the smallest

composite number

all of whose divisors (except 1) contain the digit 9.

1695 is a

rhombic

dodecahedral number.

1701 is the

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

1705 is the smallest quasi-Carmichael

number in base 4.

1715 = (1) (7)^{3} (1) (5).

1716 = _{13}C_{6}.

1722 is a

Giuga number.

1728 = 12^{3}.

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.

1755 = 3333 in base 8.

1763 is the product of

twin primes.

1764 is the

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

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

12x12 chessboard.

1789 is the smallest number with the

property that its first 4 multiples contain the digit 7.

1800 is a

pentagonal

pyramidal number.

1820 = _{16}C_{4}.

1827 is a

vampire number.

1828 is the 11^{th} meandric

number.

1834 is an

octahedral number.

1842 is the number of

rooted trees with 11

vertices.

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 C_{14}H_{30}.

1885 is a

Zeisel number.

1890 is the smallest number whose

divisors contain every digit at least four times.

1900 is the largest

palindrome in

Roman numerals.

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.

1915 is the number of

semigroups of order 5.

1925 is a

hexagonal

pyramidal number.

1947 is the number of

planar partitions

of 16.

1953 is a

Kaprekar constant

in base 2.

1958 is the number of

partitions of 25.

1960 is the

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

1980 is the number of ways to fold a 2x4

rectangle of stamps.

1990 is a

stella

octangula number.

2000 = 5555 in base 7.

2002 = _{14}C_{5}.

2008 is a

Kaprekar constant

in base 3.

2020 is a curious number.

2024 = _{24}C_{3}.

2025 is a

square that remains

square if all its

digits are incremented.

2030 is the smallest number that can be

written as a sum of 3 or 4 consecutive

squares.

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.

2047 is the smallest

composite

Mersenne number

with prime exponent.

2048 is the smallest 11^{th}

power (besides 1).

2053 is the largest known value of n for

which the product of the first n

primes - 1 is

prime.

2073 is a

Genocchi number.

2082 is the sum of its

proper divisors

that contain the digit 4.

2100 is divisible by its reverse.

2133 is a

2-hyperperfect

number.

2143 is the number of

commutative

semigroups of order 6.

2176 is the number of prime

knots with 12 crossings.

2178 is the only number known which when

multiplied by its reverse yields a fourth power.

2182 is the number of degree 15

irreducible

polynomials over GF(2).

2184 = _{14}P_{3}.

2186 = 2222222 in base 3.

2187 = 3^{7}.

2188 is the 10^{th}

Motzkin number.

2197 = 13^{3}.

2201 is the only non-palindrome

known to have a

palindromic cube.

2203 is the exponent of a

Mersenne prime.

2207 is the 16^{th}

Lucas number.

2208 is a

Keith number.

2210 = _{47}C_{2} + _{47}C_{2} + _{47}C_{1} + _{47}C_{0}.

2213 = 2^{3} + 2^{3} + 13^{3}.

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.

2255 is an

octahedral number.

2261 = 2222 + 22 + 6 + 11.

2263 = 2222 + 2 + 6 + 33.

2272 has a

cube that is a

concatenation of other

cubes.

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 4^{th}

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 = _{25}C_{3}.

2304 is the number of edges in a 9

dimensional hypercube.

2310 is the product of the first 5

primes.

2318 is the number of

connected

planar graphs with

10 edges.

2322 is the number of

connected graphs

with 10 edges.

2328 is the number of

groups of order 128.

2331 is a

centered cube

number.

2336 is the number of sided

11-iamonds.

2340 = 4444 in base 8.

2343 = 33333 in base 5.

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.

2380 = _{17}C_{4}.

2400 = 6666 in base 7.

2401 is the 4^{th} power of the

sum of its digits.

2427 = 2^{1} + 4^{2} + 2^{3}

+ 7^{4}.

2431 is the product of 3 consecutive

primes.

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.

2460 = 3333 in base 9.

2465 is a

Carmichael number.

2499 is the number of

connected

planar

Eulerian graphs

with 10 vertices.

2500 is the number of sided

9-ominoes.

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.

2532 = 2222 + 55 + 33 + 222.

2538 has a

square with 5/7 of

the digits are the same.

2550 is a

Kaprekar constant

in base 4.

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 18^{th}

Fibonacci number

.

2592 = 2^{5} 9^{2}.

2600 = _{26}C_{3}.

2601 is a

pentagonal

pyramidal number.

2606 is the number of

polyhedra with 9

vertices.

2615 is the number of functions from 9

unlabeled points to themselves.

2620 is an

amicable number.

2621 = 2222 + 66 + 222 + 111.

2623 = 2222 + 66 + 2 + 333.

2636 is a non-palindrome

with a palindromic

square.

2646 is the

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

2651 is a

stella

octangula number.

2657 is the largest known value of n for

which the product of the first n

primes + 1 is

prime.

2662 is a

palindrome and

the 2662^{nd}

triangular number

is a palindrome.

2673 is the smallest number that can be

written as the sum of 3 4^{th} powers in 2 ways.

2680 is the number of different

arrangements of 11 non-attacking queens on an 11x11 chessboard.

2683 is the largest n so that **Q**(n)

has class number 5.

2697 and its product with 5 contain every

digit from 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 n^{th}

prime and the

primes surrounding

it.

2728 is a

Kaprekar number.

2730 = _{15}P_{3}.

2736 is an

octahedral number.

2737 = (2 * 7)^{3} - 7.

2744 = 14^{3}.

2745 divides the sum of the

primes less than it.

2758 has the property that placing the

last digit first gives 1 more than triple it.

2780 = 1^{8} + 2^{7} + 3^{6}

+ 4^{5} + 5^{4} + 6^{3} + 7^{2} + 8^{1}.

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.

2821 is a

Carmichael number.

2842 is the smallest number with the

property that its first 4 multiples contain the digit 8.

2856 is a

hexagonal

pyramidal number.

2880 is the smallest number that can be

written in the form (a^{2}-1)(b^{2}-1) in 3 ways.

2890 is the smallest number in base 9

whose square

contains the same digits in the same proportion.

2916 is the product of the

squares of a subset

of its digits.

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 = _{27}C_{3}.

2931 is the reverse of the sum of its

proper substrings.

2938 is the number of

binary

rooted trees with 17

vertices.

2955 has a 5^{th} power whose

digits all occur twice.

2970 is a

harmonic

divisor number.

2996 = 2222 + 99 + 9 + 666.

2997 = 222 + 999 + 999 + 777.

2999 = 2 + 999 + 999 + 999.

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### #7

Đăng vào: 27 February 2005 - 07:23 AM

3003 is the only number

known to appear 8 times in

Pascal's triangle.

3010 is the number of

partitions of 27.

3012 is the sum of its

proper divisors

that contain the digit 5.

3024 = _{9}P_{4}.

3025 is the sum of the first 10

cubes.

3036 is the sum of its

proper divisors

that contain the digit 5.

3059 is a

centered cube

number.

3060 = _{18}C_{4}.

3068 is the number of

10-ominoes that tile

the plane.

3069 is a

Kaprekar constant

in base 2.

3078 is a

pentagonal

pyramidal number.

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 = _{22}C_{3} + _{22}C_{1} + _{22}C_{0} + _{22}C_{3}.

3106 is both the sum of the digits of

the 16^{th} and the 17^{th}

Mersenne prime.

3110 = 22222 in base 6.

3120 is the product of the first 6

Fibonacci numbers.

3124 = 44444 in base 5.

3125 = 5^{5}.

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.

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.

3174 is the sum of its

proper divisors

that contain the digit 5.

3187 and its product with 8 contain every

digit from 1-9 exactly once.

3212 = 3^{7} + 2^{9} + 1^{7}

+ 2^{9}.

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.

3254 = 33 + 2222 + 555 + 444.

3259 = 33 + 2222 + 5 + 999.

3276 = _{28}C_{3}.

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.

3301 is a value of n for which the n^{th}

Fibonacci number

begins with the digits in n.

3318 has exactly the same digits in 3

different bases.

3333 is a

repdigit.

3334 is the number of

12-iamonds.

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 = _{16}P_{3}.

3367 is the smallest number which can be

written as the difference of 2

cubes in 3 ways.

3369 is a

Kaprekar constant

in base 4.

3375 is a

cube containing only

odd digits.

3400 is a

truncated

tetrahedral number.

3413 = 1^{1} + 2^{2} + 3^{3}

+ 4^{4} + 5^{5}.

3417 is a

hexagonal

pyramidal number.

3420 is the order of a non-cyclic

simple group.

3432 is the 7^{th}

central

binomial coefficient.

3435 = 3^{3} + 4^{4} + 3^{3}

+ 5^{5}.

3439 is a

rhombic

dodecahedral number.

3444 is a

stella

octangula number.

3465 is the smallest number with the

property that its first 5 multiples contain the digit 3.

3468 = 68^{2} - 34^{2}.

3492 is the number of labeled

semigroups of order 4.

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.

3527 is the number of ways to fold a strip

of 10 stamps.

3536 is a

heptagonal

pyramidal number.

3571 is the 17^{th}

Lucas number.

3577 is a

Kaprekar constant

in base 2.

3599 is the product of

twin primes.

3610 is a

pentagonal

pyramidal number.

3624 is the smallest number n where n

through n+1 are all products of 4 or more

primes.

3645 is the maximum

determinant of a 12

x 12 matrix of 0's and 1's.

3654 = _{29}C_{3}.

3655 is the sum of consecutive

squares in 2 ways.

3684 is a

Keith number.

3685 = (3^{6} + 8) * 5.

3697 is the smallest number in base 6

whose square

contains the same digits in the same proportion.

3718 is the number of

partitions of 28.

3740 is the sum of consecutive

squares in 2 ways.

3743 is the number of

polyaboloes with 9

half squares.

3763 is the largest n so that **Q**(n)

has class number 6.

3784 has a factorization using the same

digits as itself.

3786 = 3^{4} + 7^{4} + 8

+ 6^{4}.

3792 occurs in the middle of its

square.

3825 is a

Kaprekar constant

in base 2.

3836 is the maximum number of

inversions

in a permutation of

length 7.

3840 = 10!!.

3864 = 3 * (-8 + 6^{4}).

3873 is a

Kaprekar constant

in base 4.

3876 = _{19}C_{4}.

3882 is the sum of its

proper divisors

that contain the digit 4.

3894 is an

octahedral number.

3906 = 111111 in base 5.

3911 and its reverse are

prime, even if we

append or prepend a 3 or 9.

3920 = (5+1)(5+9)(5+2)(5+0).

3925 is a

centered cube

number.

3926 is the 12^{th} meandric

number.

3937 is a

Kaprekar constant

in base 2.

3969 is a

Kaprekar constant

in base 2.

3972 = 3 + (9 * 7)^{2}.

3977 has its largest

proper divisor as

a substring.

3985 = 3333 + 9 + 88 + 555.

4006 = _{14}C_{4} + _{14}C_{0} + _{14}C_{0} + _{14}C_{6}.

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.

4051 is the number of

partitions of 6 items

into ordered lists.

4060 = _{30}C_{3}.

4062 is the smallest number with the

property that its first 8 multiples contain the digit 2.

4080 = _{17}P_{3}.

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 4^{th} powers.

4100 = 5555 in base 9.

4104 can be written as the sum of 2

cubes in 2 ways.

4128 is the smallest number with the

property that its first 10 multiples contain the digit 2.

4140 is the 8^{th}

Bell number.

4150 = 4^{5} + 1^{5} + 5^{5}

+ 0^{5}.

4151 = 4^{5} + 1^{5} + 5^{5}

+ 1^{5}.

4152 = 4^{5} + 1^{5} + 5^{5}

+ 2.

4153 = 4^{5} + 1^{5} + 5^{5}

+ 3.

4154 = 4^{5} + 1^{5} + 5^{5}

+ 4.

4155 = 4^{5} + 1^{5} + 5^{5}

+ 5.

4156 = 4^{5} + 1^{5} + 5^{5}

+ 6.

4157 = 4^{5} + 1^{5} + 5^{5}

+ 7.

4158 = 4^{5} + 1^{5} + 5^{5}

+ 8>.

4159 = 4^{5} + 1^{5} + 5^{5}

+ 9.

4160 = 4^{3} + 16^{3} + 0^{3}.

4161 = 4^{3} + 16^{3} + 1^{3}.

4181 is the first

composite number

in the Fibonacci

sequence with a

prime index.

4186 is a

hexagonal,

13-gonal,

triangular number.

4199 is the product of 3 consecutive

primes.

4200 is divisible by its reverse.

4207 is the number of

cubic graphs with 16

vertices.

4224 is a

palindrome

that is one less than a

square.

4231 is the number of labeled

partially

ordered sets with 5 elements.

4233 is a

heptagonal

pyramidal number.

4243 = 444 + 22 + 444 + 3333.

4253 is the exponent of a

Mersenne prime.

4293 has exactly the same digits in 3

different bases.

4305 has exactly the same digits in 3

different bases.

4310 has exactly the same digits in 3

different bases.

4320 = (6+4)(6+1)(6+2)(6+0).

4332 = 444 + 3333 + 333 + 222.

4335 = 444 + 3333 + 3 + 555.

4336 = 4 + 3333 + 333 + 666.

4339 = 4 + 3333 + 3 + 999.

4347 is a

heptagonal pentagonal number.

4356 is two thirds of its reversal.

4357 is the smallest number with the

property that its first 5 multiples contain the digit 7.

4368 = _{16}C_{5}.

4381 is a

stella

octangula number.

4396 = (157)(28) and each digit is

contained in the equation exactly once.

4409 is

prime, but changing

any digit makes it

composite.

4423 is the exponent of a

Mersenne prime.

4425 is the sum of the first 5 5^{th}

powers.

4434 is the sum of its

proper divisors

that contain the digit 7.

4444 is a

repdigit.

4489 is a

square whose digits

are non-decreasing.

4495 = _{31}C_{3}.

4505 is a

Zeisel number.

4506 is the sum of its

proper divisors

that contain the digit 5.

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.

4535 is the number of unlabeled

topologies with

7 elements.

4536 is the

Stirling number of the first kind s(9,6).

4548 is the sum of its

proper divisors

that contain the digit 7.

4565 is the number of

partitions of 29.

4576 is a

truncated

tetrahedral number.

4579 is an

octahedral number.

4607 is a

Woodall number.

4609 = 4444 + 66 + 0 + 99.

4613 is the number of

graphs with 10 edges.

4620 is the largest order of a

permutation of 30 or

31 elements.

4624 = 4^{4} + 4^{6} + 4^{2}

+ 4^{4}.

4641 is a

rhombic

dodecahedral number.

4655 is the number of

10-ominoes.

4665 = 33333 in base 6.

4676 is the sum of the first 7 4^{th}

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.

4713 is a

Cullen number.

4734 is the sum of its

proper divisors

that contain the digit 7.

4750 is a

hexagonal

pyramidal number.

4752 = (4+4)(4+7)(4+5)(4+2).

4760 is the sum of consecutive

squares in 2 ways.

4766 is the number of

rooted trees with 12

vertices.

4788 is a

Keith number.

4793 = 4444 + 7 + 9 + 333.

4807 is the smallest quasi-Carmichael

number in base 10.

4845 = _{20}C_{4}.

4851 is a

pentagonal

pyramidal number.

4862 is the 9^{th}

Catalan number.

4863 is the smallest number that cannot

be written as the sum of 273 8^{th} powers.

4890 is the sum of the first 4 6^{th}

powers.

4896 = _{18}P_{3}.

4900 is the only number which is both

square and

square

pyramidal (besides 1).

4913 is the

cube of the sum of

its digits.

4920 = 6666 in base 9.

4941 is a

centered cube

number.

4960 = _{32}C_{3}.

4974 is the sum of its

proper divisors

that contain the digit 8.

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### #8

Đăng vào: 27 February 2005 - 07:24 AM

5005 is the smallest

palindromic

product of 4 consecutive

primes.

5016 is a

heptagonal

pyramidal number.

5020 is an

amicable number.

5039 is the number of

planar partitions

of 18.

5040 = 7!

5041 is the largest

square known of the

form n!+1.

5050 is the sum of the first 100

integers.

5054 = 555 + 0 + 55 + 4444.

5055 has exactly the same digits in 3

different bases.

5100 is divisible by its reverse.

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.

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.

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 = 5! + (1+6)! + 8.

5169 = 5! + (1+6)! + 9.

5183 is the product of

twin primes.

5187 is the only number n known for

which phi(n-1) =

phi(n) =

phi(n+1).

5200 is divisible by its reverse.

5244 is the sum of consecutive

squares in 2 ways.

5269 is the number of

binary

rooted trees with 18

vertices.

5274 is the sum of its

proper divisors

that contain the digit 7.

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.

5400 is divisible by its reverse.

5434 is the sum of consecutive

squares in 2 ways.

5456 and its reverse are

tetrahedral

numbers.

5460 is the largest order of a

permutation of 32 or

33 elements.

5474 is a

stella

octangula number.

5477 and its reverse are both one more

than a square.

5525 is the smallest number that can be

written as the sum of 2

squares in 6 ways.

5530 is a

hexagonal

pyramidal number.

5555 is a

repdigit.

5564 is an

amicable number.

5566 is a

pentagonal

pyramidal number.

5600 is a

Kaprekar constant

in base 6.

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.

5682 is the sum of its

proper divisors

that contain the digit 4.

5693 = 5555 + 6 + 99 + 33.

5696 = 5555 + 66 + 9 + 66.

5700 is divisible by its reverse.

5719 is a

Zeisel number.

5723 has the property that its

square starts with

its reverse.

5740 = 7777 in base 9.

5775 is the product of two different

substrings of its digits.

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

Cullen number.

5796 = (138)(42) and each digit is

contained in the equation exactly once.

5798 is the 11^{th}

Motzkin number.

5814 = _{19}P_{3}.

5823 and its triple contain every digit

from 1-9 exactly once.

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.

5872 = 5555 + 88 + 7 + 222.

5880 is the

Stirling number of the second kind S(10,7).

5890 is a

heptagonal

pyramidal number.

5906 is the smallest number which is the

sum of 2 rational 4^{th} powers but is not the sum of two integer 4^{th}

powers.

5913 = 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.

5940 is divisible by its reverse.

5963 = 5555 + 9 + 66 + 333.

5972 is the smallest number that appears

in its factorial 8 times.

5974 is the number of

connected

planar graphs with 8

vertices.

5984 = _{34}C_{3}.

5985 = _{21}C_{4}.

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.

6006 is the smallest

palindrome

with 5 different prime

factors.

6008 = _{14}C_{6} + _{14}C_{0} + _{14}C_{0} + _{14}C_{8}.

6020 is the number of

Hamiltonian graphs

with 8 vertices.

6048 is the order of a non-cyclic

simple group.

6072 is the order of a non-cyclic

simple group.

6084 is the sum of the first 12

cubes.

6095 is a

rhombic

dodecahedral number.

6102 is the largest number n known where

phi(n) is the

the reverse of n.

6119 is a

centered cube

number.

6141 is a

Kaprekar constant

in base 2.

6144 = (6) (1) (4) (4)^{4}.

6174 is the

Kaprekar constant

for 4-digit numbers.

6176 is the last 4-digit sequence to

appear in the decimal expansion of

.

6181 is an

octahedral number.

6188 = _{17}C_{5}.

6200 is a

harmonic

divisor number.

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.

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.

6257 is the number of essentially different

ways to dissect a 20-gon

into 9 quadrilaterals.

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.

6348 is a

pentagonal

pyramidal number.

6368 is an

amicable number.

6380 is a value of n for which n!+1 is

prime.

6389 is the number of

functional graphs

on 11 vertices.

6391 is a

hexagonal

pyramidal number.

6400 is a

square whose digits

are non-increasing.

6435 = _{15}C_{7}.

6455 = (6^{4} - 5) * 5.

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

pi(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

pi(n).

6511 is a number n whose sum of the

factorials of its digits is equal to

pi(n).

6521 is a number n whose sum of the

factorials of its digits is equal to

pi(n).

6524 has the property that its

square starts with

its reverse.

6545 and its reverse are

tetrahedral

numbers.

6556 is the largest

palindrome

that can be made using 5 digits and the 4 arithmetic operations.

6560 is the smallest number n where n and

n+1 are both products of 7 or more

primes.

6561 = 3^{8}.

6572 is the number of

9-hexes.

6578 is the smallest number which can be

written as the sum of 3 4^{th} powers in 2 ways.

6588 is the number of sided

12-iamonds.

6593 = 6 + 5555 + 999 + 33.

6601 is a

Carmichael number.

6611 is a

Cullen number.

6620 is the number of

11-ominoes that tile

the plane.

6636 has exactly the same digits in 3

different bases.

6643 is the smallest number which is

palindromic in

bases 2 and 3.

6666 is a

repdigit.

6667 is the number of self-dual

planar graphs with

24 edges.

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 = _{8}P_{5}.

6729 and its double together use each of

the digits 1-9 exactly once.

6735 is a

stella

octangula number.

6765 is the 20^{th}

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.

6840 = _{20}P_{3}.

6842 is the number of

partitions of 31.

6859 = 19^{3}.

6860 is a

heptagonal

pyramidal number.

6864 = 6666 + 88 + 66 + 44.

6880 is a

vampire number.

6888 has a

square with 3/4 of

the digits are the same.

6889 is a

strobogrammatic

square.

6912 = (6) (9) (1) (2)^{7}.

6922 is the number of

polycubes containing 8

cubes.

6940 is the sum of its

proper divisors

that contain the digit 3.

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 is

contained in the equation exactly once.

6953 = 66 + 999 + 5555 + 333.

6966 is the number of

planar graphs with 8

vertices.

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### #9

Đăng vào: 27 February 2005 - 07:25 AM

7106 is an

octahedral number.

7140 is the largest number which is both

triangular and

tetrahedral.

7161 is a

Kaprekar constant

in base 2.

7192 is an

abundant number

that is not the sum of some subset of its divisors.

7200 is a

pentagonal

pyramidal number.

7230 is the sum of consecutive

squares in 2 ways.

7254 = (186)(39) and each digit is

contained in the equation exactly once.

7272 is a

Kaprekar number.

7314 is the smallest number so that it

and its successor are products of 4

primes.

7315 = _{22}C_{4}.

7318 is the number of functions from 10

unlabeled points to themselves.

7337 is a

hexagonal

pyramidal number.

7381 = 11111 in base 9.

7385 is a

Keith number.

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 6x6

alternating

sign matrices.

7471 is a

centered cube

number.

7494 is the sum of its

proper divisors

that contain the digit 4.

7496 = 777 + 44 + 9 + 6666.

7512 is the sum of its

proper divisors

that contain the digit 5.

7549 is the largest known

prime p where no

numbers of the form p-n^{2} are

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.

7595 is the number of simplicial

polyhedra with 12

vertices.

7647 is a

Keith number.

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.

7683 is a

truncated

tetrahedral number.

7693 is a value of n for which the sum

of the first n primes is a

palindrome.

7710 is the number of degree 17

irreducible

polynomials over GF(2).

7734 is the sum of its

proper divisors

that contain the digit 8.

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.

7770 = _{37}C_{3}.

7775 = 55555 in base 6.

7776 is a 5^{th} power whose

digits are non-increasing.

7777 is a

Kaprekar number.

7800 is the order of a non-cyclic

simple group.

7810 has the property that its

square is the

concatenation of two consecutive numbers.

7812 = 222222 in base 5.

7825 is a

rhombic

dodecahedral number.

7851 = 7777 + 8 + 55 + 11.

7852 = (1963)(4) and each digit is

contained in the equation exactly once.

7856 = 7777 + 8 + 5 + 66.

7905 is a

Kaprekar constant

in base 2.

7909 is a

Keith number.

7920 is the order of the smallest

sporadic group.

7931 is a

heptagonal

pyramidal number.

7936 is the 9^{th}

Euler number.

7941 = 7777 + 9 + 44 + 111.

7942 = 7777 + 99 + 44 + 22.

7946 = 7777 + 99 + 4 + 66.

7980 is the smallest number whose

divisors contain every digit at least 7 times.

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.

8008 = _{16}C_{6}.

8026 is the number of

planar partitions

of 19.

8042 is the largest number known which

cannot be written as a sum of 7 or fewer

cubes.

8071 is the number of

connected graphs

with 11 edges.

8100 is divisible by its reverse.

8119 is an

octahedral number.

8125 is the smallest number that can be

written as the sum of 2

squares in 5 ways.

8128 is the 4^{th}

perfect number.

8176 is a

stella

octangula number.

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 13^{th}

power (besides 1).

8208 = 8^{4} + 2^{4} + 0^{4}

+ 8^{4}.

8226 is the sum of its

proper divisors

that contain the digit 4.

8281 is the only 4-digit

square whose two

2-digit pairs are consecutive.

8349 is the number of

partitions of 32.

8372 is a

hexagonal

pyramidal number.

8375 is the smallest number which has

equal numbers of every digit in bases 2 and 6.

8400 is divisible by its reverse.

8403 = 33333 in base 7.

8415 is the smallest number which has

equal numbers of every digit in bases 3 and 6.

8436 = _{38}C_{3}.

8486 = 888 + 44 + 888 + 6666.

8510 is a value of n for which the sum

of the first n primes is a

palindrome.

8538 is the sum of its

proper divisors

that contain the digit 4.

8562 is the sum of its

proper divisors

that contain the digit 4.

8568 = _{18}C_{5}.

8586 has exactly the same digits in 3

different bases.

8614 and its

prime factors

contain every digit from 1-9 exactly once.

8664 = 888 + 6666 + 666 + 444.

8682 is the sum of its

proper divisors

that contain the digit 4.

8712 is 4 times its reverse.

8732 has exactly the same digits in 3

different bases.

8736 is the smallest number that appears

in its factorial 10 times.

8753 = 88 + 7777 + 555 + 333.

8758 = 88 + 7777 + 5 + 888.

8763 and its successor have the same

digits in their prime

factorization.

8772 is the sum of the first 8 4^{th}

powers.

8778 is a

palindromic

triangular number.

8826 is the sum of its

proper divisors

that contain the digit 4.

8833 = 88^{2} + 33^{2}.

8855 = _{23}C_{4}.

8888 is a

repdigit.

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.

8964 is the smallest number with the

property that its first 6 multiples contain the digit 8.

8970 = 8 + 9^{4} + 7^{4}

+ 0.

8971 = 8 + 9^{4} + 7^{4}

+ 1.

8972 = 8 + 9^{4} + 7^{4}

+ 2.

8973 = 8 + 9^{4} + 7^{4}

+ 3.

8974 = 8 + 9^{4} + 7^{4}

+ 4.

8975 = 8 + 9^{4} + 7^{4}

+ 5.

8976 = 8 + 9^{4} + 7^{4}

+ 6.

8977 = 8 + 9^{4} + 7^{4}

+ 7.

8978 = 8 + 9^{4} + 7^{4}

+ 8.

8979 = 8 + 9^{4} + 7^{4}

+ 9.

9009 is a

centered cube

number.

9012 is the sum of its

proper divisors

that contain the digit 5.

9091 is the only

prime known whose

reciprocal has period 10.

9108 is a

heptagonal

pyramidal number.

9126 is a

pentagonal

pyramidal number.

9139 = _{39}C_{3}.

9174 is the sum of its

proper divisors

that contain the digit 5.

9189 is the number of sided

10-ominoes.

9224 is an

octahedral number.

9233 is the number of different

arrangements (up to rotation and reflection) of 13 non-attacking queens on a

13x13 chessboard.

9240 = _{22}P_{3}.

9253 is the smallest number that appears

in its factorial 9 times.

9261 = 21^{3}.

9272 is an

abundant number

that is not the sum of some subset of its divisors.

9330 is the

Stirling number of the second kind S(10,3).

9331 = 111111 in base 6.

9349 is the 19^{th}

Lucas number.

9362 = 22222 in base 8.

9376 is an

automorphic number.

9385 is the sum of consecutive

squares in 2 ways.

9386 = 99 + 333 + 8888 + 66.

9408 is the number of reduced 6 x 6

Latin squares.

9451 is the number of

binary

rooted trees with 19

vertices.

9468 is the sum of its

proper divisorsproper

divisors that contain the digit 7.

9474 = 9^{4} + 4^{4} + 7^{4}

+ 4^{4}.

9477 is the maximum

determinant of a 13

x 13 matrix of 0's and 1's.

9496 is the number of 10x10

symmetric

permutation

matrices.

9500 is a

hexagonal

pyramidal number.

9563 = 9 + 5555 + 666 + 3333.

9568 = 9 + 5 + 666 + 8888.

9608 is the number of

digraphs with 5

vertices.

9625 has a

square formed by

inserting a block of digits inside itself.

9653 = 99 + 666 + 5555 + 3333.

9658 = 99 + 666 + 5 + 8888.

9660 is a

truncated

tetrahedral number.

9689 is the exponent of a

Mersenne prime.

9726 is the smallest number in base 5

whose square

contains the same digits in the same proportion.

9784 is the number of 2 state

Turing machines

which halt.

9789 is the smallest number that appears

in its factorial 11 times.

9801 is 9 times its reverse.

9809 is a

stella

octangula number.

9828 is the order of a non-cyclic

simple group.

9841 = 111111111 in base 3.

9855 is a

rhombic

dodecahedral number.

9862 is the number of

knight's tours on a

6 x 6 chess board.

9876 is the largest 4-digit number with

different digits.

9880 = _{40}C_{3}.

9901 is the only

prime known whose

reciprocal has period 12.

9941 is the exponent of a

Mersenne prime.

9976 has a

square formed by

inserting a block of digits inside itself.

9988 is the number of prime

knots with 13 crossings.

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.

9999 is a

Kaprekar number.

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### #10

Đăng vào: 17 March 2006 - 06:51 PM

trời đất bro tonami viết dài thía nhóc đọc mỏi cả mắt...

### #11

Đăng vào: 07 April 2006 - 04:12 AM

trùi ui ! đọc còn chưa hết nửa sao mà dịch đây !

### #12

Đăng vào: 06 January 2007 - 09:14 PM

Khung?_kieu? nay` doc xong ngat' xiu? mat'