A031557 Numbers k such 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 59.

3483, 3491, 3499, 3511, 3527, 3539, 3547, 3559, 3571, 3579, 3583, 3587, 3607, 3623, 3631, 3643, 3647, 3651, 3659, 3667, 3671, 3691, 3699, 3707, 3719, 13928, 13952, 13960, 13984, 14016, 14080, 14120, 14152, 14176, 14208, 14216, 14240, 14248, 14304

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Mathematica

cfep59Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 59]; Select[Range[15000], cfep59Q] (* Harvey P. Dale, Feb 18 2016 *)

Prog

(Python)
from __future__ import division
from sympy import continued_fraction_periodic
A031557_list = [n for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in range(1, 10**5)) if isinstance(s, list) and len(s) % 2 == 0 and s[len(s)//2-1] == 59] # Chai Wah Wu, Jun 08 2017

Crossrefs

Sequence in context: A176380 A156773 A174753 * A031737 A268156 A180994

Adjacent sequences: A031554 A031555 A031556 * A031558 A031559 A031560

Keyword

nonn

Author

David W. Wilson

Status

approved