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

1,1

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A036353 A174769 A031597 * A237064 A251977 A196897

Adjacent sequences: A031774 A031775 A031776 * A031778 A031779 A031780

Keyword

nonn

Author

David W. Wilson

Status

approved