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A031423 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 10.

%I A031423 #33 Sep 16 2021 14:54:33
%S A031423 701,1418,1493,2197,2290,3257,4793,6154,6466,8389,8753,9577,9965,
%T A031423 10765,11257,11677,12541,14218,14929,15413,15658,16001,16501,17009,
%U A031423 17786,18049,18314,18581,19121,21577,22157,22745,24557,24677,25805,26561,27530,28517
%N A031423 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 10.
%H A031423 Chai Wah Wu, <a href="/A031423/b031423.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe and Georg Fischer)
%t A031423 n = 1; t = {}; While[Length[t] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[OddQ[len] && c[[2, (len + 1)/2]] == 10 && c[[2, (len + 1)/2 - 1]] == 10, AppendTo[t, n]]]]; t (* _T. D. Noe_, Apr 04 2014; corrected by _Georg Fischer_, Jun 23 2019 *)
%o A031423 (Python)
%o A031423 from sympy.ntheory.continued_fraction import continued_fraction_periodic
%o A031423 A031423_list = []
%o A031423 for n in range(1,10**4):
%o A031423     cf = continued_fraction_periodic(0,1,n)
%o A031423     if len(cf) > 1 and len(cf[1]) > 1 and len(cf[1]) % 2 and cf[1][len(cf[1])//2] == 10:
%o A031423         A031423_list.append(n) # _Chai Wah Wu_, Sep 16 2021
%Y A031423 Cf. A031404-A031422.
%Y A031423 Subsequence of A003814.
%K A031423 nonn
%O A031423 1,1
%A A031423 _David W. Wilson_
%E A031423 a(1) corrected by _T. D. Noe_, Apr 04 2014
%E A031423 a(1) = 26 removed by _Georg Fischer_, Jun 23 2019