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%I #17 Jul 13 2023 19:07:03
%S 10002,10006,10018,10022,10046,10054,10078,10082,10086,10102,10118,
%T 10134,10146,10162,10174,10178,10182,10194,10198,10214,10226,10238,
%U 10274,10278,10294,10306,10326,10334,10338,10342,10358,10402,22503,22521,22548,22557
%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 100.
%H Chai Wah Wu, <a href="/A031598/b031598.txt">Table of n, a(n) for n = 1..10000</a>
%t cf100Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{1},ContinuedFraction[s][[2]]];len= Length[ cf];EvenQ[len]&&cf[[(len)/2]]==100]; Select[Range[23000],cf100Q]
%o (Python)
%o from __future__ import division
%o from sympy import continued_fraction_periodic
%o A031598_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] == 100] # _Chai Wah Wu_, Jun 10 2017
%K nonn
%O 1,1
%A _David W. Wilson_
%E Definition corrected by _Harvey P. Dale_, Jul 13 2023
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