cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A025332 Numbers that are the sum of 3 nonzero squares in 4 or more ways.

Original entry on oeis.org

129, 134, 146, 153, 161, 171, 189, 194, 198, 201, 206, 209, 230, 234, 243, 246, 249, 251, 254, 257, 261, 266, 269, 270, 278, 281, 285, 290, 293, 294, 297, 299, 306, 314, 321, 326, 329, 339, 341, 342, 350, 353, 354, 362, 363, 365, 369, 371, 374, 378, 381, 386, 387, 389
Offset: 1

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A023051 Numbers that are the sum of two positive cubes in at least four ways (all solutions).

Original entry on oeis.org

6963472309248, 12625136269928, 21131226514944, 26059452841000, 55707778473984, 74213505639000, 95773976104625, 101001090159424, 159380205560856, 169049812119552, 174396242861568, 188013752349696
Offset: 1

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Author

David W. Wilson (revised Oct 15 1997)

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, D1.

Crossrefs

Extensions

b-file extended by Ray Chandler, Jan 19 2009

A025296 Numbers that are the sum of 2 nonzero squares in 5 or more ways.

Original entry on oeis.org

5525, 8125, 8450, 9425, 10625, 11050, 12025, 12325, 13325, 14365, 14450, 15725, 16250, 17225, 17425, 18125, 18785, 18850, 19825, 21125, 21250, 22100, 22525, 23125, 23725, 24050, 24505, 24650, 25625, 25925, 26650, 26825, 27625, 28730, 28925, 29725
Offset: 1

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Programs

  • Maple
    N:= 10^5: # generate all entries <=N
    V:= Vector(N,datatype=integer[4]):
    for a from 1 to floor(sqrt(N)) do
      for b from a do
        n:= a^2 + b^2;
        if n > N then break fi;
        V[n]:= V[n]+1
    od od:
    select(t -> V[t] >= 5, [$1..N]); # Robert Israel, Jun 01 2025
  • Mathematica
    nn = 30000; t = Table[0, {nn}]; lim = Floor[Sqrt[nn - 1]]; Do[num = i^2 + j^2; If[num <= nn, t[[num]]++], {i, lim}, {j, i}]; Flatten[Position[t, ?(# >= 5 &)]] (* _T. D. Noe, Apr 07 2011 *)

A025314 Numbers that are the sum of 2 distinct nonzero squares in 4 or more ways.

Original entry on oeis.org

1105, 1625, 1885, 2125, 2210, 2405, 2465, 2665, 3145, 3250, 3445, 3485, 3625, 3770, 3965, 4225, 4250, 4420, 4505, 4625, 4745, 4810, 4930, 5125, 5185, 5330, 5365, 5525, 5785, 5945, 6205, 6290, 6305, 6409, 6500, 6565, 6625, 6890, 6970, 7085, 7225, 7250
Offset: 1

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Comments

Subsequence of A025295. But sequences A025295 and A025314 are different, A025295(346) = 31250 = 175^2 + 25^2 = 161^2 + 73^2 = 155^2 + 85^2 = 125^2 + 125^2 (not distinct squares) is not in A025314. - Vaclav Kotesovec, Feb 27 2016
Numbers in A025295 but not in A025314 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^6 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^6 = 31250 is the smallest term in A025295 that is not in A025314. - Chai Wah Wu, Feb 27 2016

Programs

  • Mathematica
    nn = 7250; t = Table[0, {nn}]; lim = Floor[Sqrt[nn - 1]]; Do[num = i^2 + j^2; If[num <= nn, t[[num]]++], {i, lim}, {j, i - 1}]; Flatten[Position[t, ?(# >= 4 &)]] (* _T. D. Noe, Apr 07 2011 *)
Showing 1-4 of 4 results.