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.

A025285 Numbers that are the sum of 2 nonzero squares in exactly 2 ways.

Original entry on oeis.org

50, 65, 85, 125, 130, 145, 170, 185, 200, 205, 221, 250, 260, 265, 290, 305, 338, 340, 365, 370, 377, 410, 442, 445, 450, 481, 485, 493, 500, 505, 520, 530, 533, 545, 565, 578, 580, 585, 610, 625, 629, 680, 685, 689, 697, 730, 740, 745, 754, 765, 785, 793, 800, 820
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Order and signs don't count. E.g. 50 = 5^2+5^2 = 7^2+1^2 (= (-5)^2+5^2, but that doesn't count as different).
A131574 is a subsequence. - Zak Seidov, Jan 31 2014
A025426(a(n)) = 2. - Reinhard Zumkeller, Feb 26 2015

Links

Crossrefs

Cf. A025284, A025286, A025287, A025288, A025289, A025290, A025291, A025292, A025293, A025426.
Cf. A007692.

Programs

  • Haskell
    a025285 n = a025285_list !! (n-1)
a025285_list = filter ((== 2) . a025426) [1..]
-- Reinhard Zumkeller, Feb 26 2015
  • Mathematica
    selQ[n_] := Length[ Select[ PowersRepresentations[n, 2, 2], Times @@ # != 0 &]] == 2; Select[Range[1000], selQ] (* Jean-François Alcover, Oct 03 2013 *)
  • PARI
    is(n)=sum(k=sqrtint((n-1)\2)+1,sqrtint(n-1), issquare(n-k^2))==2 \\ Charles R Greathouse IV, May 24 2016
  • PARI
    is(n)=my(v=valuation(n, 2), f=factor(n>>v), t=1); for(i=1, #f[, 1], if(f[i, 1]%4==1, t*=f[i, 2]+1, if(f[i, 2]%2, return(0)))); if(t%2, t-(-1)^v, t)==4 \\ Charles R Greathouse IV, May 24 2016

Formula

a(n) >= A007692(n) with equality only for n <= 16. - Alois P. Heinz, Mar 23 2023

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025289, A025296, A025298, A025334.

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 *)

A025307 Numbers that are the sum of 2 distinct nonzero squares in exactly 6 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, 28730, 28925, 29725, 31025, 31265, 31450, 31525, 32825, 34450, 34645, 34850, 35425, 36125
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Where does this first differ from A025289? - R. J. Mathar, Jun 24 2025

Links

Programs

  • Mathematica
    nn = 36125; 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, 6]] (* T. D. Noe, Apr 07 2011 *)
Showing 1-3 of 3 results.

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

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