A031588 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 90.

8102, 8114, 8126, 8158, 8166, 8182, 8194, 8198, 8222, 8254, 8258, 8262, 8278, 8302, 8306, 8318, 8338, 8342, 8402, 8406, 8414, 8422, 8434, 8438, 8454, 8462, 18228, 18237, 18273, 18291, 18294, 18366, 18372, 18393, 18399, 18417, 18429, 18453, 18489, 18507

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Mathematica

cf90Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]]==90]; Select[Range[20000], cf90Q] (* Harvey P. Dale, Mar 30 2020 *)

Crossrefs

Sequence in context: A172775 A172843 A258541 * A145657 A224727 A163045

Adjacent sequences: A031585 A031586 A031587 * A031589 A031590 A031591

Keyword

nonn

Author

David W. Wilson

Status

approved