A031597 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 99.

9803, 9811, 9839, 9843, 9851, 9859, 9871, 9883, 9887, 9899, 9907, 9923, 9931, 9959, 9963, 9967, 9987, 9991, 10007, 10019, 10031, 10039, 10067, 10079, 10083, 10091, 10099, 10103, 10107, 10111, 10131, 10139, 10147, 10151, 10159, 10163, 10199, 39208

Offset

1,1

Links

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

Mathematica

ep99Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[s][[2]]]; len= Length[ cf]; EvenQ[len]&&cf[[len/2]]==99]; Select[Range[40000], ep99Q] (* Harvey P. Dale, May 07 2023 *)

Prog

(Python)
from __future__ import division
from sympy import continued_fraction_periodic
A031597_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] == 99] # Chai Wah Wu, Jun 10 2017

Crossrefs

Sequence in context: A113937 A036353 A174769 * A031777 A237064 A251977

Adjacent sequences: A031594 A031595 A031596 * A031598 A031599 A031600

Keyword

nonn

Author

David W. Wilson

Extensions

Definition corrected by Harvey P. Dale, May 07 2023

Status

approved