A031634 - OEIS

A031634

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 46.

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

%S 4909,26293,26618,44602,65657,66685,91373,120634,153953,154738,156314,

%T 157898,193961,238585,281429,283553,286754,289973,332401,333554,

%U 334709,335866,338186,341681,344021,345194,387613,395113,400153,447065

%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 46.

%t cf46Q[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]] == cf[[(len+1)/2]]==46]; Select[Range[500000],cf46Q] (* _Harvey P. Dale_, Apr 14 2020 *)

%K nonn

%O 1,1

%A _David W. Wilson_

%E First term 2117 removed by _Georg Fischer_, Jun 16 2019