A048610 Smallest number that is the sum of two positive squares in >= n ways.

2, 50, 325, 1105, 5525, 5525, 27625, 27625, 71825, 138125, 160225, 160225, 801125, 801125, 801125, 801125, 2082925, 2082925, 4005625, 4005625, 5928325, 5928325, 5928325, 5928325, 29641625, 29641625, 29641625, 29641625, 29641625, 29641625

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v, Jud McCranie

Keywords

• nonn
• nice

Examples

			2 = 1^2 + 1^2; 50 = 1^2 + 7^2 = 5^2 + 5^2; 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2 + 15^2.
		

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 50, p. 19, Ellipses, Paris 2008.
• J. Meeus, Problem 1375, J. Rec. Math., 18 (No. 1, 1985), p. 70.
• Problem 590, J. Rec. Math., 11 (No. 2, 1978), p. 137.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..96
• J. Meeus, Note
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A016032, A007511, A052199, A071383.

Programs

Mathematica

(* Assuming a(n) multiple of 1105, from 1105 on, to speed up computation *) twoSquaresR[n_] := twoSquaresR[n] = With[{r = Reduce[0 < x <= y && n == x^2 + y^2, {x, y}, Integers]}, If[r === False, 0, Length[{x, y} /. {ToRules[r]}]]]; a[n_] := a[n] = For[an = a[n - 1], True, an = If[an < 1105, an + 1, an + 1105], If[ twoSquaresR[an] >= n, Return[an]]];a[1] = 2; Table[ Print[a[n]]; a[n], {n, 1, 30}] (* Jean-François Alcover, Jun 22 2012 *)
nn = 10^6; t2 = Table[0, {nn}]; n2 = Floor[Sqrt[nn]]; Do[r = a^2 + b^2; If[r <= nn, t2[[r]]++], {a, n2}, {b, a, n2}]; t = {}; n = 1; While[a = Position[t2, ?(# >= n &), 1, 1]; a != {}, AppendTo[t, a[[1, 1]]]; n++]; t (* _T. D. Noe, Jun 22 2012 *)