A048610 Smallest number that is the sum of two positive squares in >= n ways. (Formerly M2172)

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

1,1

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

Example

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.

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 *)

Crossrefs

Cf. A016032, A007511, A052199, A071383.

Sequence in context: A318094 A226408 A226337 * A007511 A016032 A080299

Adjacent sequences: A048607 A048608 A048609 * A048611 A048612 A048613

Keyword

nonn,nice

Author

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

Status

approved