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

1,1

Links

Table of n, a(n) for n=1..34.

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 *)

Crossrefs

Subsequence of A003814.

Sequence in context: A290644 A231289 A212725 * A350047 A043579 A166780

Adjacent sequences: A031605 A031606 A031607 * A031609 A031610 A031611

Keyword

nonn

Author

David W. Wilson

Extensions

First term 401 removed by Georg Fischer, Jun 16 2019

Status

approved