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    #1 tonami

    tonami

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    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. happy.gif




    #2 tonami

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    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 xy=yx
    with x and y different integers.

    17 is the number of
    wallpaper groups.

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

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

    20 is the number 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 2nd
    perfect number.

    29 is the 7th
    Lucas number.

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

    31 is a
    Mersenne prime.

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

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

    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 5th
    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 |2x - 3y|.

    42 is the 5th
    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 6th
    Motzkin number.

    52 is the 5th
    Bell number.

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

    54 is the smallest 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 4th
    power is of the form a4+b4-c4.

    60 is the smallest number divisible by 1
    through 6.

    61 is the 6th
    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 n2
    and n3 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 12+22+12+...+n2
    = 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 = 81 + 92

    90 is the number of degrees in a right angle.

    91 is the smallest
    pseudoprime in base
    3.

    92 is the number of different arrangements
    of 8 non-attacking queens on an 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 - 2k is
    prime for k>1.

    106 is the number of
    trees with 10 vertices.

    107 is the exponent of a
    Mersenne prime.

    108 is 3
    hyperfactorial.

    109 is the smallest number which is
    palindromic 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+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 10th
    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 = 9C4.

    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 = 8C1 + 8C3
    + 8C4.

    135 = 11 + 32 + 53.

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

    137 is the maximum number of 7th
    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 nth
    prime
    is square.

    151 is a
    palindromic prime.

    152 ???

    153 = 13 + 53 + 33.

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

    155 is the sum of the
    primes 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 C11H24.

    160 is the number of
    9-iamonds.

    161 is a
    hexagonal
    pyramidal number
    .

    162 ???

    163 is the largest
    Heegner Number.

    164 ???

    165 = 11C3.

    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 = 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 ???

    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
    2nCn 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 11th
    Lucas number.

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

     



    #3 tonami

    tonami

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    Đăng vào: 27 February 2005 - 07:17 AM

    201 is a
    Kaprekar constant
    in base 4.

    202 ???

    203 is the 6th
    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 4th 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 = 35.

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

    245 is a
    stella
    octangula number
    .

    246 = 9C2 + 9C4
    + 9C6.

    247 is the smallest possible difference
    between two integers that together contain each 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 5th
    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 8th 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 9th 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 7th
    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 5th
    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 = 25 + 8 + 35.

    284 is an
    amicable number.

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

    286 is the number of
    rooted trees with 9
    vertices.

    287 ???

    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 12th
    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 = 11C4.

    333 is the number of
    7-hexes.

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

    336 = 8P3.

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

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

    355 is the number of labeled
    topologies with
    4 elements.

    360 is the number of degrees in a circle.

    364 = 14C3.

    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 = 33 + 73 + 03.

    371 = 33 + 73 + 13.

    372 is a
    hexagonal
    pyramidal number
    .

    373 is a permutable
    prime.

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

    375 is a
    truncated
    tetrahedral number
    .

    376 is an
    automorphic number.

    377 is the 14th
    Fibonacci number.

    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.

     



    #4 tonami

    tonami

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    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 = 43 + 03 + 73.

    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 7th
    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 a1+...+an=(a1)...(an).

    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 = 15C3.

    456 is the number of
    tournaments with 7
    vertices.

    461 = 444 + 6 + 11.

    462 = 11C5.

    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 3rd
    perfect number.

    497 is the number of
    graphs with 8 edges.

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

    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 = 9P3.

    505 = 10C5 +
    10
    C0 + 10C5.

    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 = 51 + 12 + 83.

    521 is the 13th
    Lucas number.

    525 is a
    hexagonal
    pyramidal number
    .

    527 is the smallest number n for which
    there do not exist 4 smaller numbers a1 through a4 so that
    a1! a2! a3! a4! 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 10th 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 = 16C3.

    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 7th
    power can be written as the sum of 7 7th 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 = 15 + 29 + 34.

    595 is a
    palindromic
    triangular number.

    598 = 51 + 92 + 83.

    607 is the exponent of a
    Mersenne prime.

    610 is the 15th
    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 225+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 = 12+22+12+...+k2 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 = 11C6 +
    11
    C8 + 11C2.

    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 = 13C4.

    718 is the number of unlabeled
    topologies with
    6 elements.

    719 is the number of
    rooted trees with 10
    vertices.

    720 = 6!

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

    724 is the number of different arrangements
    of 10 non-attacking queens on an 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 = 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 = 7 + 3! + (3!)!.

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

    736 = 7 + 36.

    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 = 17 + 24 + 36.

    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 n2
    = mC0 + mC1 + mC2
    + mC3 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 6th
    powers.

    797 is the number of
    functional graphs
    on 9 vertices.

    800 = 2222 in base 7.

     




    #5 tonami

    tonami

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    Đăng vào: 27 February 2005 - 07:20 AM


    802 is the number of
    isomers of C13H28.

    810 is divisible by its reverse.

    816 = 18C3.

    820 = 1111 in base 9.

    822 is the number of
    planar graphs with 7
    vertices.

    835 is the 9th
    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 14th
    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 7th
    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 6th
    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 = 93 + 53 + 23
    + (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 4th
    powers.

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

    986 = 19 + 28 + 36.

    987 is the 16th
    Fibonacci number.

    990 = 11P3.

    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 = 103.

    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 = 81 + 80 + 83
    + 83.

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

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

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

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

    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 8th
    power can be written as the sum of 9 8th 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 17
    + 27 + 37 + 07 equals 1230 written in base 8.

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

    1233 = 122 + 332.

    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 = 13C5.

    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 5th
    powers.

    1301 is the number of
    trees with 13 vertices.

    1306 = 11 + 32 + 03
    + 64.

    1320 = 12P3.

    1330 = 21C3.

    1331 is a
    cube containing only
    odd digits.

    1364 is the 15th
    Lucas number.

    1365 = 15C4.

    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 = 12 + 372 + 02.

    1371 = 12 + 372 + 12.

    1376 is the smallest number with the
    property that it and its neighbors are not
    cubefree.

    1385 is the 8th
    Euler number.

    1386 = 1 + 34 + 8 + 64.

    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 8th
    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 e1467
    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).

     





    #6 tonami

    tonami

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    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 17th
    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 = 14 + 64 + 34
    + 44.

    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 = 11 + 62 + 73
    + 64.

    1680 is the smallest number with 40
    divisors.

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

    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 = 13C6.

    1722 is a
    Giuga number.

    1728 = 123.

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

    1730 is the sum of consecutive
    squares in 2 ways.

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

    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 = 16C4.

    1827 is a
    vampire number.

    1828 is the 11th 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 C14H30.

    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 = 14C5.

    2008 is a
    Kaprekar constant
    in base 3.

    2020 is a curious number.

    2024 = 24C3.

    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 11th
    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 = 14P3.

    2186 = 2222222 in base 3.

    2187 = 37.

    2188 is the 10th
    Motzkin number.

    2197 = 133.

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

    2203 is the exponent of a
    Mersenne prime.

    2207 is the 16th
    Lucas number.

    2208 is a
    Keith number.

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

    2213 = 23 + 23 + 133.

    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 4th
    powers.

    2281 is the exponent of a
    Mersenne prime.

    2285 is a non-palindrome
    with a palindromic
    square.

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

    2300 = 25C3.

    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 = 17C4.

    2400 = 6666 in base 7.

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

    2427 = 21 + 42 + 23
    + 74.

    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 18th
    Fibonacci number
    .

    2592 = 25 92.

    2600 = 26C3.

    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 2662nd
    triangular number
    is a palindrome.

    2673 is the smallest number that can be
    written as the sum of 3 4th powers in 2 ways.

    2680 is the number of different
    arrangements of 11 non-attacking queens on an 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 nth
    prime and the
    primes surrounding
    it.

    2728 is a
    Kaprekar number.

    2730 = 15P3.

    2736 is an
    octahedral number.

    2737 = (2 * 7)3 - 7.

    2744 = 143.

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

    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 (a2-1)(b2-1) 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 = 27C3.

    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 5th 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.

     





    #7 tonami

    tonami

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    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 = 9P4.

    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 = 18C4.

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

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

    3110 = 22222 in base 6.

    3120 is the product of the first 6
    Fibonacci numbers.

    3124 = 44444 in base 5.

    3125 = 55.

    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 = 37 + 29 + 17
    + 29.

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

    3217 is the exponent of a
    Mersenne prime.

    3254 = 33 + 2222 + 555 + 444.

    3259 = 33 + 2222 + 5 + 999.

    3276 = 28C3.

    3280 = 11111111 in base 3.

    3281 is the sum of consecutive
    squares in 2 ways.

    3282 is the sum of its
    proper divisors
    that contain the digit 4.

    3301 is a value of n for which the nth
    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 = 16P3.

    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 = 11 + 22 + 33
    + 44 + 55.

    3417 is a
    hexagonal
    pyramidal number
    .

    3420 is the order of a non-cyclic
    simple group.

    3432 is the 7th
    central
    binomial coefficient
    .

    3435 = 33 + 44 + 33
    + 55.

    3439 is a
    rhombic
    dodecahedral number
    .

    3444 is a
    stella
    octangula number
    .

    3465 is the smallest number with the
    property that its first 5 multiples contain the digit 3.

    3468 = 682 - 342.

    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 17th
    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 = 29C3.

    3655 is the sum of consecutive
    squares in 2 ways.

    3684 is a
    Keith number.

    3685 = (36 + 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 = 34 + 74 + 8
    + 64.

    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 + 64).

    3873 is a
    Kaprekar constant
    in base 4.

    3876 = 19C4.

    3882 is the sum of its
    proper divisors
    that contain the digit 4.

    3894 is an
    octahedral number.

    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 12th 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 = 14C4 +
    14
    C0 + 14C0 + 14C6.

    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 = 30C3.

    4062 is the smallest number with the
    property that its first 8 multiples contain the digit 2.

    4080 = 17P3.

    4095 = 111111111111 in base 2.

    4096 is the smallest number with 13
    divisors.

    4097 is the smallest number (besides 2)
    that can be written as the sum of two
    cubes or the sum of
    two 4th powers.

    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 8th
    Bell number.

    4150 = 45 + 15 + 55
    + 05.

    4151 = 45 + 15 + 55
    + 15.

    4152 = 45 + 15 + 55
    + 2.

    4153 = 45 + 15 + 55
    + 3.

    4154 = 45 + 15 + 55
    + 4.

    4155 = 45 + 15 + 55
    + 5.

    4156 = 45 + 15 + 55
    + 6.

    4157 = 45 + 15 + 55
    + 7.

    4158 = 45 + 15 + 55
    + 8>.

    4159 = 45 + 15 + 55
    + 9.

    4160 = 43 + 163 + 03.

    4161 = 43 + 163 + 13.

    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 = 16C5.

    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 5th
    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 = 31C3.

    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 = 44 + 46 + 42
    + 44.

    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 4th
    powers.

    4681 = 11111 in base 8.

    4683 is the number of orderings of 6
    objects with ties allowed.

    4705 is the sum of consecutive
    squares in 2 ways.

    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 = 20C4.

    4851 is a
    pentagonal
    pyramidal number
    .

    4862 is the 9th
    Catalan number.

    4863 is the smallest number that cannot
    be written as the sum of 273 8th powers.

    4890 is the sum of the first 4 6th
    powers.

    4896 = 18P3.

    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 = 32C3.

    4974 is the sum of its
    proper divisors
    that contain the digit 8.

     




    #8 tonami

    tonami

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    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 11th
    Motzkin number.

    5814 = 19P3.

    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 4th powers but is not the sum of two integer 4th
    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 = 34C3.

    5985 = 21C4.

    5986 and its
    prime factors
    contain every digit from 1-9 exactly once.

    5993 is the largest number known which
    is not the sum of a
    prime
    and twice a
    square
    .

    5994 is the number of
    lattices on 10 unlabeled
    nodes.

    5995 is a
    palindromic
    triangular number.

    5996 is a
    truncated
    tetrahedral number
    .

    6001 has a
    cube that is a
    concatenation of other
    cubes
    .

    6006 is the smallest
    palindrome
    with 5 different prime
    factors
    .

    6008 = 14C6 +
    14
    C0 + 14C0 + 14C8.

    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 = 17C5.

    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 = 15C7.

    6455 = (64 - 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 = 38.

    6572 is the number of
    9-hexes.

    6578 is the smallest number which can be
    written as the sum of 3 4th powers in 2 ways.

    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 = 8P5.

    6729 and its double together use each of
    the digits 1-9 exactly once.

    6735 is a
    stella
    octangula number
    .

    6765 is the 20th
    Fibonacci number.

    6769 is the

    Stirling number of the first kind
    s(8,4).

    6772 = 6666 + 7 + 77 + 22.

    6779 = 6666 + 7 + 7 + 99.

    6788 is the smallest number with

    multiplicative persistence
    6.

    6840 = 20P3.

    6842 is the number of
    partitions of 31.

    6859 = 193.

    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.

     





    #9 tonami

    tonami

      Free like the wind

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    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 = 22C4.

    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-n2 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 = 37C3.

    7775 = 55555 in base 6.

    7776 is a 5th 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 9th
    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 = 16C6.

    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 4th
    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 13th
    power (besides 1).

    8208 = 84 + 24 + 04
    + 84.

    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 = 38C3.

    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 = 18C5.

    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 4th
    powers.

    8778 is a
    palindromic
    triangular number.

    8826 is the sum of its
    proper divisors
    that contain the digit 4.

    8833 = 882 + 332.

    8855 = 23C4.

    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 + 94 + 74
    + 0.

    8971 = 8 + 94 + 74
    + 1.

    8972 = 8 + 94 + 74
    + 2.

    8973 = 8 + 94 + 74
    + 3.

    8974 = 8 + 94 + 74
    + 4.

    8975 = 8 + 94 + 74
    + 5.

    8976 = 8 + 94 + 74
    + 6.

    8977 = 8 + 94 + 74
    + 7.

    8978 = 8 + 94 + 74
    + 8.

    8979 = 8 + 94 + 74
    + 9.

    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 = 39C3.

    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 = 22P3.

    9253 is the smallest number that appears
    in its factorial 9 times.

    9261 = 213.

    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 19th
    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 = 94 + 44 + 74
    + 44.

    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 = 40C3.

    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.

     




    #10 thangnhosieuway

    thangnhosieuway

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    Đăng vào: 17 March 2006 - 06:51 PM

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

    #11 haquyen

    haquyen

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    Đăng vào: 07 April 2006 - 04:12 AM

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

    #12 giang224

    giang224

      Người bạn mới đến

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    Đăng vào: 06 January 2007 - 09:14 PM

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




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