A031419 - OEIS

A031419

Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 6.

%I #22 Aug 18 2021 00:33:16

%S 109,281,865,922,1277,1613,1769,1933,2161,2341,2789,3098,3653,3961,

%T 4285,4457,5065,5153,5713,5858,5954,6101,6458,6554,6709,7129,7349,

%U 7681,8237,8941,9242,9305,9677,10177,10498,10565,10693,10762,11162,11365,11698

%N Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 6.

%H T. D. Noe, <a href="/A031419/b031419.txt">Table of n, a(n) for n = 1..1000</a> [shifted by _Georg Fischer_, Jun 23 2019]

%t n = 1; t = {}; While[Length[t] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[OddQ[len] && c[[2, (len + 1)/2]] == 6 && c[[2, (len + 1)/2 - 1]] == 6, AppendTo[t, n]]]]; t (* _T. D. Noe_, Apr 04 2014; corrected by _Georg Fischer_, Jun 23 2019 *)

%Y Cf. A031404-A031423.

%Y Subsequence of A003814.

%K nonn

%O 1,1

%A _David W. Wilson_

%E a(1) corrected by _T. D. Noe_, Apr 04 2014

%E a(1) = 10 removed by _Georg Fischer_, Jun 23 2019