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A031777 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) 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
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 22 02:28 EDT 2024. Contains 373561 sequences. (Running on oeis4.)