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A031413 Numbers n such that continued fraction for sqrt(n) has even period 2*m and the m-th term is 10. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See comment to A031551.  From 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: A046293 A241179 A096924 * A127665 A097037 A035480

Adjacent sequences:  A031410 A031411 A031412 * A031414 A031415 A031416

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)