A031777 - OEIS

%I #20 Jul 11 2021 21:36:53

%S 9803,39208,88215,156824,245035,352848,480263,627280,793899,980120,

%T 1185943,1411368,1656395,1921024,2205255,2509088,2832523,3175560,

%U 3538199,3920440,4322283,4743728,5184775,5645424,6125675,6625528,7144983,7684040

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

%C (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

%H Chai Wah Wu, <a href="/A031777/b031777.txt">Table of n, a(n) for n = 1..10000</a>

%t 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 *)

%o (Python)

%o from sympy import continued_fraction_periodic

%o 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

%K nonn

%O 1,1

%A _David W. Wilson_