A031563 that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 65.

4227, 4231, 4243, 4247, 4259, 4271, 4283, 4299, 4307, 4319, 4327, 4339, 4363, 4391, 4411, 4419, 4423, 4443, 4447, 4451, 4463, 4467, 4483, 4487, 16904, 16928, 16936, 16992, 17000, 17024, 17056, 17088, 17096, 17120, 17128, 17152, 17216, 17224, 17248

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Mathematica

cf65Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 65]; Select[Range[17300], cf65Q] (* Harvey P. Dale, Dec 29 2019 *)

Crossrefs

Sequence in context: A097226 A202488 A167037 * A031743 A236725 A345580

Adjacent sequences: A031560 A031561 A031562 * A031564 A031565 A031566

Keyword

nonn

Author

David W. Wilson

Status

approved