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%I #16 Aug 18 2021 00:15:36
%S 102,114,118,134,142,228,237,249,273,309,321,404,412,428,436,452,460,
%T 476,492,500,508,524,540,548,556,572,630,645,655,670,695,705,745,755,
%U 805,820,830,895,906,1002,1038,1050,1146,1182,1194,1232,1253,1290,1337
%N 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.
%C See comment to A031551. - _Harvey P. Dale_, Jul 10 2012
%H T. D. Noe, <a href="/A031413/b031413.txt">Table of n, a(n) for n = 1..1000</a>
%t 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 *)
%t 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 *)
%Y Cf. A031404-A031423.
%K nonn
%O 1,1
%A _David W. Wilson_
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