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Values of n at which the period of the continued fraction for sqrt(n) is nondecreasing.
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%I #8 Dec 12 2015 16:48:23

%S 1,2,3,6,7,13,19,21,22,31,43,46,76,94,124,133,139,151,166,211,214,244,

%T 301,309,331,421,526,571,604,631,751,886,919,991,1279,1291,1324,1366,

%U 1516,1621,1726,2011,2311,2566,2671,3004,3019,3259,3334,3691,3931,4174

%N Values of n at which the period of the continued fraction for sqrt(n) is nondecreasing.

%t t = {1}; mx = 0; n = 1; While[Length[t] < 60, n++; If[! IntegerQ[Sqrt[n]], len = Length[ContinuedFraction[Sqrt[n]][[2]]]; If[len >= mx, AppendTo[t, n]; mx = len]]]; t (* _T. D. Noe_, Dec 10 2013 *)

%Y Superset of A013645.

%K nonn

%O 1,2

%A _David Spies_, Dec 09 2013

%E Extended by _T. D. Noe_, Dec 10 2013