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 1-3 of 3 results.

A025338 Numbers that are the sum of 3 nonzero squares in 10 or more ways.

Original entry on oeis.org

594, 734, 761, 794, 801, 846, 854, 866, 881, 909, 926, 941, 950, 965, 986, 1001, 1026, 1034, 1041, 1046, 1049, 1089, 1106, 1109, 1121, 1130, 1154, 1161, 1169, 1181, 1190, 1206, 1209, 1214, 1226, 1238, 1265, 1274, 1286, 1301, 1314, 1322, 1326, 1329, 1341
Offset: 1

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Crossrefs

A025320 Numbers that are the sum of 2 distinct nonzero squares in 10 or more ways.

Original entry on oeis.org

138125, 160225, 204425, 226525, 235625, 276250, 292825, 300625, 308125, 320450, 333125, 337025, 348725, 359125, 386425, 393125, 403325, 408850, 416585, 430625, 435625, 453050, 456025, 469625, 471250, 491725, 493025, 495625, 499525, 505325
Offset: 1

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Comments

Subsequence of A025301. But sequences A025320 and A025301 are different. 2*5^18 = 7629394531250 = 182125^2 + 2756125^2 = 390625^2 + 2734375^2 = 596875^2 + 2696875^2 = 799687^2 + 2643841^2 = 946555^2 + 2594885^2 = 1140625^2 + 2515625^2 = 1328125^2 + 2421875^2 = 1507975^2 + 2314175^2 = 1799375^2 + 2095625^2 = 1953125^2 + 1953125^2 (not distinct squares) is not in A025320. - Vaclav Kotesovec, Feb 27 2016
Numbers in A025301 but not in A025320 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^18 where p_i are primes of the form 4*k+3 and q is a prime of the form 4*k+1. Thus 2*5^18 is the smallest term in A025301 that is not in A025320. - Chai Wah Wu, Feb 27 2016

Crossrefs

Cf. A025301. - R. J. Mathar, Oct 23 2008

Programs

  • Mathematica
    nn = 505325; 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, ?(# >= 10 &)]] (* _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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Crossrefs

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 *)
Showing 1-3 of 3 results.