A031554 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 56.

3138, 3142, 3154, 3158, 3166, 3186, 3214, 3218, 3222, 3238, 3254, 3262, 3266, 3282, 3298, 3326, 3334, 3362, 7059, 7113, 7149, 7167, 7197, 7203, 7233, 7239, 7269, 7278, 7284, 7311, 7329, 7341, 7347, 7356, 7377, 7401, 7419, 7422, 7428, 7449, 7494, 7509

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Mathematica

cf56Q[n_]:=Module[{s=Sqrt[n], cf}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; EvenQ[Length[cf]]&&cf[[Length[cf]/2]]==56]; Select[ Range[ 7600], cf56Q] (* Harvey P. Dale, Apr 28 2013 *)

Crossrefs

Sequence in context: A176790 A086103 A267721 * A180297 A187645 A187640

Adjacent sequences: A031551 A031552 A031553 * A031555 A031556 A031557

Keyword

nonn

Author

David W. Wilson

Status

approved