

A031777


Numbers n such that least term in period of continued fraction for sqrt(n) is 99.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



