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

Author

David W. Wilson

Keywords

• nonn

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

Programs

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 *)

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