A031641 - OEIS

A031641

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 53.

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

%S 17981,35018,35393,57202,58162,58645,85385,161026,163441,209138,

%T 210053,254377,258425,260461,262505,372629,376298,384929,441521,

%U 444181,446849,448186,450866,454901,516253,522013,530713,596825,603017,606125,609241

%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 53.

%t cf53Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1,1}, ContinuedFraction[ s][[2]]];len=Length[cf];OddQ[len]&&cf[[(len+1)/2]] == 53]; Select[Range[610000],cf53Q] (* _Harvey P. Dale_, Jul 14 2017 *)

%K nonn

%O 1,1

%A _David W. Wilson_

%E Corrected and extended by _Harvey P. Dale_, Jul 14 2017