A031777 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 99.

9803, 39208, 88215, 156824, 245035, 352848, 480263, 627280, 793899, 980120, 1185943, 1411368, 1656395, 1921024, 2205255, 2509088, 2832523, 3175560, 3538199, 3920440, 4322283, 4743728, 5184775, 5645424, 6125675, 6625528, 7144983, 7684040

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

(99*m)^2+2*m for m >= 1 is a proper subsequence (it is a subsequence, see comment in A031749) as the term 97042400 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

lt99Q[n_]:=Module[{s=Sqrt[n],lt},If[IntegerQ[s],lt=1,lt= Min[ ContinuedFraction[ s][[2]]]];lt==99]; Select[Range[8000000],lt99Q] (* Harvey P. Dale, Apr 20 2013 *)

Python

from sympy import continued_fraction_periodic
A031777_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) == 99] # Chai Wah Wu, Jun 10 2017