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
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
KEYWORD
nonn,nice
STATUS
approved