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%I #20 Aug 19 2021 23:23:20
%S 3,7,8,15,24,32,35,48,63,75,80,88,91,99,115,120,135,136,143,168,175,
%T 176,195,208,215,224,247,255,279,280,288,304,312,319,323,360,399,403,
%U 427,432,440,464,483,528,539,551,555,560,575,595,611,624,671,675,696
%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 1.
%H T. D. Noe, <a href="/A031404/b031404.txt">Table of n, a(n) for n = 1..1000</a>
%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]] == 1, AppendTo[t, n]]]]; t (* _T. D. Noe_, Apr 04 2014 *)
%Y Cf. A031405-A031423.
%K nonn
%O 1,1
%A _David W. Wilson_
%E Names of A031404-A031423 clarified by _N. J. A. Sloane_, Aug 18 2021