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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 9.
2

%I #17 Aug 18 2021 00:33:16

%S 601,1073,1930,2017,2621,2825,3037,3533,3769,4013,4714,5701,6218,6373,

%T 6689,7013,7757,8461,8825,9197,9277,12629,13394,13621,14081,14549,

%U 15613,15754,18265,18797,20005,20282,20441,21410,22277,22993,23762,24065,24370,25114

%N 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 9.

%H T. D. Noe, <a href="/A031422/b031422.txt">Table of n, a(n) for n = 1..1000</a>

%t 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]] == 9, AppendTo[t, n]]]]; t (* _T. D. Noe_, Apr 04 2014 *)

%Y Cf. A031404-A031423.

%Y Subsequence of A003814.

%K nonn

%O 1,1

%A _David W. Wilson_

%E a(1) removed by _T. D. Noe_, Apr 04 2014