A031608 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 20.

2729, 5233, 8362, 8917, 24874, 29873, 31973, 37997, 38777, 46237, 54818, 56698, 57173, 58129, 64129, 64634, 65141, 66161, 66674, 67189, 67706, 68746, 74713, 87277, 88457, 89645, 90841, 100186, 101450, 104002, 104645, 115333, 116689, 126541

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Crossrefs

Subsequence of A003814.

Programs

Mathematica

cf20Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1,1},ContinuedFraction[ s][[2]]];len=Length[cf];OddQ[len]&&cf[[Floor[len/2]]] == cf[[Ceiling[len/2]]] ==20]; Select[ Range[ 130000],cf20Q] (* Harvey P. Dale, Sep 18 2021 *)

Extensions

First term 401 removed by Georg Fischer, Jun 16 2019