A031561 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 63.

3971, 4003, 4007, 4019, 4027, 4039, 4051, 4059, 4079, 4083, 4091, 4099, 4111, 4127, 4131, 4139, 4151, 4159, 4183, 4207, 4211, 4219, 4223, 15880, 15936, 15944, 15968, 15976, 16000, 16064, 16160, 16192, 16224, 16232, 16288, 16328, 16424, 16480, 16544

Offset

1,1

Comments

The "central term" is the term appearing at 1/2 the length of the period of the continued fraction, not the term succeeding that term. For instance, the periodic part of the continued fraction of sqrt(4139) is {2, 1, 63, 1, 2, 128}. - Harvey P. Dale, Sep 07 2012

Links

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

Mathematica

ct63Q[n_]:=Module[{sqrt=Sqrt[n], cf, len}, cf=If[IntegerQ[sqrt], {1}, ContinuedFraction[sqrt][[2]]]; len=Length[cf]; EvenQ[len] && cf[[len/2]]==63]; Select[ Range[17000], ct63Q] (* Harvey P. Dale, Sep 07 2012 *)

Crossrefs

Sequence in context: A343024 A343002 A230067 * A031741 A204501 A204494

Adjacent sequences: A031558 A031559 A031560 * A031562 A031563 A031564

Keyword

nonn

Author

David W. Wilson

Status

approved