A031775 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 97.

9411, 37640, 84687, 150552, 235235, 338736, 461055, 602192, 762147, 940920, 1138511, 1354920, 1590147, 1844192, 2117055, 2408736, 2719235, 3048552, 3396687, 3763640, 4149411, 4554000, 4977407, 5419632, 5880675, 6360536, 6859215, 7376712

Offset

1,1

Comments

(97*m)^2+2*m for m >= 1 are terms of the sequence (see comment in A031749). The term 89453959 is not of this form. - Chai Wah Wu, Jun 19 2016

Links

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

Mathematica

cf97Q[n_]:=Module[{s=Sqrt[n]}, If[IntegerQ[s], 1, Min[ContinuedFraction[s][[2]]]]==97]; Select[Range[738*10^4], cf97Q] (* Harvey P. Dale, Nov 20 2018 *)

Prog

(Python)
from sympy import continued_fraction_periodic
A031775_list = [n for n, d in ((n, continued_fraction_periodic(0, 1, n)[-1]) for n in range(1, 10**5)) if isinstance(d, list) and min(d) == 97] # Chai Wah Wu, Jun 10 2017

Crossrefs

Sequence in context: A206251 A264340 A031595 * A143367 A234432 A235677

Adjacent sequences: A031772 A031773 A031774 * A031776 A031777 A031778

Keyword

nonn

Author

David W. Wilson

Status

approved