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.

A025335 Numbers that are the sum of 3 nonzero squares in 7 or more ways.

Original entry on oeis.org

341, 369, 374, 446, 461, 486, 494, 506, 509, 521, 545, 549, 566, 569, 581, 594, 614, 621, 626, 629, 641, 654, 666, 677, 686, 689, 701, 710, 726, 729, 731, 734, 749, 761, 770, 774, 789, 794, 797, 801, 806, 809, 810, 818, 821, 825, 833, 846, 849, 854, 857, 866, 869, 881
Offset: 1

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A025297 Numbers that are the sum of 2 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

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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}]; Flatten[Position[t, ?(# >= 6 &)]] (* _T. D. Noe, Apr 07 2011 *)

A025299 Numbers that are the sum of 2 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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Examples

			27625 is in the sequence via 20^2 + 165^2 = 27^2 + 164^2 = 45^2 + 160^2 = 60^2 + 155^2 = 83^2 + 144^2 = 88^2 + 141^2 = 101^2 + 132^2 = 115^2 + 120^2. - _David A. Corneth_, Jun 01 2025
		

Crossrefs

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}]; Flatten[Position[t, ?(# >= 8 &)]] (* _T. D. Noe, Apr 07 2011 *)
  • PARI
    upto(n) = {my(v = vector(n)); for(i = 1, sqrtint(n), i2 = i^2; for(j = i, sqrtint(n - i^2), v[i2 + j^2]++)); select(x->x >= 8, v, 1)} \\ David A. Corneth, Jun 01 2025

A025317 Numbers that are the sum of 2 distinct 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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Comments

Subsequence of A025298. But sequences A025317 and A025298 are different. 2*5^12 = 488281250 = 15625^2 + 15625^2 (not distinct squares) = 14395^2 + 16765^2 = 10625^2 + 19375^2 = 9125^2 + 20125^2 = 4775^2 + 21575^2 = 3125^2 + 21875^2 = 1457^2 + 22049^2 is not in A025317. - Vaclav Kotesovec, Feb 27 2016
Numbers in A025298 but not in A025317 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^12 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^12 is the smallest term in A025298 that is not in A025317. - Chai Wah Wu, Feb 27 2016

Programs

  • Mathematica
    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 - 1}]; Flatten[Position[t, ?(# >= 7 &)]] (* _T. D. Noe, Apr 07 2011 *)
Showing 1-4 of 4 results.