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.

A025334 Numbers that are the sum of 3 nonzero squares in 6 or more ways.

Original entry on oeis.org

209, 297, 306, 314, 321, 326, 329, 341, 342, 369, 374, 425, 426, 434, 441, 446, 458, 459, 461, 486, 489, 494, 497, 506, 509, 513, 521, 530, 531, 534, 542, 545, 546, 549, 558, 561, 566, 569, 581, 593, 594, 602, 605, 614, 621, 626, 629, 633, 641, 649, 650, 654, 657, 659
Offset: 1

Views

Author

Keywords

Crossrefs

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

Views

Author

Keywords

Crossrefs

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 *)

A025298 Numbers that are the sum of 2 nonzero squares in 7 or more ways.

Original entry on oeis.org

27625, 32045, 40885, 45305, 47125, 55250, 58565, 60125, 61625, 64090, 66625, 67405, 69745, 71825, 77285, 78625, 80665, 81770, 86125, 87125, 90610, 91205, 93925, 94250, 98345, 98605, 99125, 99905, 101065, 105625, 107185, 110500, 111605, 112625
Offset: 1

Views

Author

Keywords

Crossrefs

Programs

  • Mathematica
    Parallelize[Select[Range[120000],Length[PowersRepresentations[#,2,2]]>6&]]  (* Harvey P. Dale, Feb 19 2011 *)
    nn = 112625; 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, ?(# >= 7 &)]] (* _T. D. Noe, Apr 07 2011 *)

A025316 Numbers that are the sum of 2 distinct nonzero squares in 6 or more ways.

Original entry on oeis.org

5525, 9425, 11050, 12025, 12325, 13325, 14365, 15725, 17225, 17425, 18785, 18850, 19825, 21125, 22100, 22525, 23725, 24050, 24505, 24650, 25925, 26650, 26825, 27625, 28730, 28925, 29725, 31025, 31265, 31450, 31525, 32045, 32825, 34450, 34645, 34850
Offset: 1

Views

Author

Keywords

Comments

Subsequence of A025297. But sequences A025316 and A025297 are different. 2*5^10 = 19531250 = 3125^2 + 3125^2 (not distinct squares) = 2879^2 + 3353^2 = 2125^2 + 3875^2 = 1825^2 + 4025^2 = 955^2 + 4315^2 = 625^2 + 4375^2 is not in A025316. - Vaclav Kotesovec, Feb 27 2016
Numbers in A025297 but not in A025316 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^10 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^10 is the smallest term in A025297 that is not in A025316. - Chai Wah Wu, Feb 27 2016

Programs

  • Mathematica
    nn = 34850; 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, ?(# >= 6 &)]] (* _T. D. Noe, Apr 07 2011 *)
Showing 1-4 of 4 results.