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%I #34 Jul 16 2021 01:34:32
%S 1025,4098,9219,16388,25605,36870,50183,65544,82953,102410,123915,
%T 147468,173069,200718,230415,262160,295953,331794,369683,409620,
%U 451605,495638,541719,589848,640025,692250,746523,802844,861213,921630,984095,1048608
%N Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 64.
%C The continued fraction expansion of sqrt((j*m)^2+t*m) for m >= 1 where t divides 2*j has the form [j*m, 2*j/t, 2*j*m, 2*j/t, 2*j*m, ...]. Thus numbers of the form (32*m)^2 + m for m >= 1 are in the sequence. Are there any others? - _Chai Wah Wu_, Jun 18 2016
%C The term 4464834 is not of the form (32*m)^2 + m. - _Chai Wah Wu_, Jun 19 2016
%H Charles R Greathouse IV, <a href="/A031742/b031742.txt">Table of n, a(n) for n = 1..10000</a>
%t okQ[n_]:=Module[{sq=Sqrt[n]},!IntegerQ[sq]&&Min[ContinuedFraction[sq][[2]]]==64]; Select[Range[1100000],okQ] (* _Harvey P. Dale_, Aug 24 2012 *)
%K nonn
%O 1,1
%A _David W. Wilson_
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