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.

A025336 Numbers that are the sum of 3 nonzero squares in 8 or more ways.

Original entry on oeis.org

374, 446, 486, 521, 566, 569, 594, 614, 621, 626, 629, 686, 689, 701, 710, 729, 734, 749, 761, 770, 774, 789, 794, 801, 809, 810, 825, 846, 849, 854, 857, 866, 869, 881, 902, 909, 914, 926, 929, 941, 945, 950, 953, 965, 969, 971, 974, 986, 989, 990, 1001, 1014, 1022
Offset: 1

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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

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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 *)

A025300 Numbers that are the sum of 2 nonzero squares in 9 or more ways.

Original entry on oeis.org

71825, 93925, 122525, 138125, 143650, 156325, 160225, 173225, 187850, 204425, 209525, 223925, 226525, 235625, 244205, 245050, 257725, 267325, 273325, 276250, 287300, 292825, 296225, 300625, 308125, 308425, 312650, 320450, 333125, 337025
Offset: 1

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Programs

  • Maple
    N:= 4*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] >= 9, [$1..N]); # Robert Israel, Jun 01 2025
  • Mathematica
    nn = 337025; 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, ?(# >= 9 &)]] (* _T. D. Noe, Apr 07 2011 *)

A025318 Numbers that are the sum of 2 distinct nonzero squares in 8 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, 107185, 110500, 111605, 112625, 114985
Offset: 1

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Comments

Subsequence of A025299. But sequences A025318 and A025299 are different. 2*5^14 = 12207031250 = 7285^2 + 110245^2 = 15625^2 + 109375^2 = 23875^2 + 107875^2 = 45625^2 + 100625^2 = 53125^2 + 96875^2 = 60319^2 + 92567^2 = 71975^2 + 83825^2 = 78125^2 + 78125^2 (not distinct squares) is not in A025318. - Vaclav Kotesovec, Feb 27 2016
Numbers in A025299 but not in A025318 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^14 or of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q_1^2*q_2^4 where p_i are distinct primes of the form 4k+3 and q_1, q_2 are distinct primes of the form 4k+1. Thus 2*5^4*13^2 = 211250 is the smallest term in A025299 that is not in A025318. - Chai Wah Wu, Feb 27 2016

Programs

  • Mathematica
    nn = 114985; 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, ?(# >= 8 &)]] (* _T. D. Noe, Apr 07 2011 *)
Showing 1-4 of 4 results.