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

1,1

Comments

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

Links

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

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 *)

Crossrefs

Cf. A031404-A031423.

Sequence in context: A241179 A096924 A354710 * A127665 A097037 A035480

Adjacent sequences: A031410 A031411 A031412 * A031414 A031415 A031416

Keyword

nonn

Author

David W. Wilson

Status

approved