A031613 - OEIS

A031613

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 25.

%I #14 Aug 18 2021 00:10:32

%S 1453,7793,13306,13537,19165,20285,28393,35569,37861,46514,47378,

%T 47813,57961,58925,60877,83473,84629,85793,86378,88738,100481,101114,

%U 101749,104309,104954,105601,114973,116329,123229,131885,133337,134797,136265,139225

%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 25.

%t cf25Q[n_]:=Module[{s=Sqrt[n],c,len},c=If[IntegerQ[s],{0,0}, ContinuedFraction[ s][[2]]];len=Length[c];OddQ[len] && c[[Floor[ len/2]+ 1]] == 25]; Select[Range[140000],cf25Q] (* _Harvey P. Dale_, Nov 22 2013 *)

%K nonn

%O 1,1

%A _David W. Wilson_

%E Corrected and extended by _Harvey P. Dale_, Nov 22 2013