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.

A025331 Numbers that are the sum of 3 nonzero squares in 3 or more ways.

Original entry on oeis.org

54, 66, 81, 86, 89, 99, 101, 110, 114, 126, 129, 131, 134, 146, 149, 150, 153, 161, 162, 166, 171, 173, 174, 179, 182, 185, 186, 189, 194, 198, 201, 206, 209, 216, 219, 221, 222, 225, 227, 230, 233, 234, 237, 241, 242, 243, 245, 246, 249, 251, 254, 257, 258, 261, 264
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A024796, A025294, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025368, A025398, A025427.

A018787 Numbers that are the sum of two positive cubes in at least three ways (all solutions).

Original entry on oeis.org

87539319, 119824488, 143604279, 175959000, 327763000, 700314552, 804360375, 958595904, 1148834232, 1407672000, 1840667192, 1915865217, 2363561613, 2622104000, 3080802816, 3235261176, 3499524728, 3623721192, 3877315533, 4750893000, 5544709352, 5602516416
Offset: 1

Views

Author

David W. Wilson, Aug 15 1996

Keywords

References

  • J. Leech, Some solutions of Diophantine equations, Proc. Camb. Phil. Soc., 53 (1957), 778-780.
  • R. K. Guy, Unsolved Problems in Number Theory, D1.

Links

Crossrefs

Cf. A001235, A003825, A023051, A025294, A025398, A344804.

Programs

  • Mathematica
    a=Sort[Flatten@Table[n^3+m^3,{m,2000},{n,m-1,1,-1}]];f3[l_]:=Module[{t={}},Do[If[l[[n]]==l[[n+2]],AppendTo[t,l[[n]]]],{n,1,Length[l]-2}];t];f3[a] (* Vladimir Joseph Stephan Orlovsky, Jan 21 2012 *)

A025295 Numbers that are the sum of 2 nonzero squares in 4 or more ways.

Original entry on oeis.org

1105, 1625, 1885, 2125, 2210, 2405, 2465, 2665, 3145, 3250, 3445, 3485, 3625, 3770, 3965, 4225, 4250, 4420, 4505, 4625, 4745, 4810, 4930, 5125, 5185, 5330, 5365, 5525, 5785, 5945, 6205, 6290, 6305, 6409, 6500, 6565, 6625, 6890, 6970, 7085, 7225, 7250
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A023051, A025287, A025294, A025296, A025332.

Programs

  • Mathematica
    nn = 7250; 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, ?(# >= 4 &)]] (* _T. D. Noe, Apr 07 2011 *)

A025313 Numbers that are the sum of 2 distinct nonzero squares in 3 or more ways.

Original entry on oeis.org

325, 425, 650, 725, 845, 850, 925, 1025, 1105, 1300, 1325, 1445, 1450, 1525, 1625, 1690, 1700, 1825, 1850, 1885, 2050, 2125, 2210, 2225, 2405, 2425, 2465, 2525, 2600, 2650, 2665, 2725, 2825, 2873, 2890, 2900, 2925, 3050, 3125, 3145, 3250, 3380, 3400
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Sequence contains no primes (A000040) and no semiprimes (A001358). - Zak Seidov, Apr 07 2011
Sequences A025294 and A025313 are different. For example 1250 is not in A025313. A025294(9) = 1250 = 35^2 + 5^2 = 31^2 + 17^2 = 25^2 + 25^2 (not distinct squares). - Vaclav Kotesovec, Feb 27 2016
Numbers in A025294 but not in A025313 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^4 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^4 = 1250 is the smallest term in A025294 that is not in A025313. - Chai Wah Wu, Feb 27 2016

Examples

			325 = 1^2+18^2 = 6^2+17^2 = 10^2+15^2. [Zak Seidov, Apr 07 2011]

Links

Programs

  • Mathematica
    nn = 3400; 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, ?(# >= 3 &)]] (* _T. D. Noe, Apr 07 2011 *)
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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