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.

A025337 Numbers that are the sum of 3 nonzero squares in 9 or more ways.

Original entry on oeis.org

594, 614, 626, 689, 734, 761, 774, 794, 801, 846, 854, 866, 881, 909, 914, 926, 929, 941, 950, 965, 974, 986, 989, 990, 1001, 1025, 1026, 1034, 1041, 1046, 1049, 1062, 1070, 1074, 1089, 1091, 1097, 1106, 1109, 1118, 1121, 1130, 1134, 1139, 1154, 1161, 1166
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A024796, A025300, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025374, A025427, A345119.

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

Views

Author

David W. Wilson

Keywords

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

Links

Crossrefs

Cf. A025291, A025298, A025300, A025336.

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

A025319 Numbers that are the sum of 2 distinct 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

Views

Author

David W. Wilson

Keywords

Comments

Subsequence of A025300. But sequences A025319 and A025300 are different. 2*5^16 = 305175781250 = 36425^2 + 551225^2 = 78125^2 + 546875^2 = 119375^2 + 539375^2 = 189311^2 + 518977^2 = 228125^2 + 503125^2 = 265625^2 + 484375^2 = 301595^2 + 462835^2 = 359875^2 + 419125^2 = 390625^2 + 390625^2 (not distinct squares) is not in A025319. - Vaclav Kotesovec, Feb 27 2016
Numbers in A025300 but not in A025319 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^16 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^16 is the smallest term in A025300 that is not in A025319. - Chai Wah Wu, Feb 27 2016

Links

Programs

  • 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 - 1}]; Flatten[Position[t, ?(# >= 9 &)]] (* _T. D. Noe, Apr 07 2011 *)

A025301 Numbers that are the sum of 2 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

Views

Author

David W. Wilson

Keywords

Comments

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 4k+3 and q is a prime of the form 4k+1. Thus 2*5^18 is the smallest term in A025301 that is not in A025320. - Chai Wah Wu, Feb 27 2016

Links

Crossrefs

Cf. A025293, A025300, A025338.

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}]; Flatten[Position[t, ?(# >= 10 &)]] (* _T. D. Noe, Apr 07 2011 *)
Showing 1-4 of 4 results.

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