A031413 Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 10.

102, 114, 118, 134, 142, 228, 237, 249, 273, 309, 321, 404, 412, 428, 436, 452, 460, 476, 492, 500, 508, 524, 540, 548, 556, 572, 630, 645, 655, 670, 695, 705, 745, 755, 805, 820, 830, 895, 906, 1002, 1038, 1050, 1146, 1182, 1194, 1232, 1253, 1290, 1337

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

See comment to A031551. - Harvey P. Dale, Jul 10 2012

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A031404-A031423.

Programs

Mathematica

epQ[n_]:=Module[{p=ContinuedFraction[Sqrt[n]][[2]],len},len=Length[p];EvenQ[len]&&p[[len/2]]==10];nn=1300;With[{trms=Complement[Range[ nn],Range[ Floor[Sqrt[nn]]]^2]},Select[trms,epQ]] (* Harvey P. Dale, Jul 10 2012 *)
n = 1; t = {}; While[Length[t] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[EvenQ[len] && c[[2, len/2]] == 10, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)