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%I #17 May 07 2023 15:18:01
%S 9803,9811,9839,9843,9851,9859,9871,9883,9887,9899,9907,9923,9931,
%T 9959,9963,9967,9987,9991,10007,10019,10031,10039,10067,10079,10083,
%U 10091,10099,10103,10107,10111,10131,10139,10147,10151,10159,10163,10199,39208
%N Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 99.
%H Chai Wah Wu, <a href="/A031597/b031597.txt">Table of n, a(n) for n = 1..10000</a>
%t ep99Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1},ContinuedFraction[s][[2]]];len= Length[ cf];EvenQ[len]&&cf[[len/2]]==99]; Select[Range[40000],ep99Q] (* _Harvey P. Dale_, May 07 2023 *)
%o (Python)
%o from __future__ import division
%o from sympy import continued_fraction_periodic
%o A031597_list = [n for n, s in ((i, continued_fraction_periodic(0,1,i)[-1]) for i in range(1,10**5)) if isinstance(s, list) and len(s) % 2 == 0 and s[len(s)//2-1] == 99] # _Chai Wah Wu_, Jun 10 2017
%K nonn
%O 1,1
%A _David W. Wilson_
%E Definition corrected by _Harvey P. Dale_, May 07 2023
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