A031598 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 100.

10002, 10006, 10018, 10022, 10046, 10054, 10078, 10082, 10086, 10102, 10118, 10134, 10146, 10162, 10174, 10178, 10182, 10194, 10198, 10214, 10226, 10238, 10274, 10278, 10294, 10306, 10326, 10334, 10338, 10342, 10358, 10402, 22503, 22521, 22548, 22557

Offset

1,1

Links

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

Mathematica

cf100Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[s][[2]]]; len= Length[ cf]; EvenQ[len]&&cf[[(len)/2]]==100]; Select[Range[23000], cf100Q]

Prog

(Python)
from __future__ import division
from sympy import continued_fraction_periodic
A031598_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] == 100] # Chai Wah Wu, Jun 10 2017

Crossrefs

Sequence in context: A364050 A360574 A330135 * A210760 A164968 A165296

Adjacent sequences: A031595 A031596 A031597 * A031599 A031600 A031601

Keyword

nonn

Author

David W. Wilson

Extensions

Definition corrected by Harvey P. Dale, Jul 13 2023

Status

approved