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A031601 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 13. 1

%I #24 Aug 18 2021 00:10:32

%S 409,1181,2258,3562,3802,3925,5305,5897,8269,9829,10834,11041,12389,

%T 15737,16745,17785,21757,23029,23633,24554,25178,26869,27194,27521,

%U 28181,28514,28849,30554,30901,32413,33853,36073,36185,40841,41362,41765,42170

%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 the two central terms are both 13.

%H Vincenzo Librandi, <a href="/A031601/b031601.txt">Table of n, a(n) for n = 1..150</a>

%t cf13Q[n_]:=Module[{per=ContinuedFraction[Sqrt[n]][[2]]},OddQ[Length[ per]]&&per[[Floor[Length[per]/2]+1]]==13]; nn=43000;With[{terms = Complement[Range[nn], Range[Floor[Sqrt[nn]]]^2]}, Select[terms, cf13Q]] (* _Harvey P. Dale_, Nov 23 2011 *)

%Y Subsequence of A003814.

%K nonn

%O 1,1

%A _David W. Wilson_

%E Corrected by _Harvey P. Dale_, Nov 23 2011

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)