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%I #13 Aug 18 2021 00:10:32
%S 1850,16909,46681,91253,151402,224797,226697,313769,316013,417541,
%T 425329,537578,540514,676045,682637,984593,990554,994538,1158401,
%U 1162709,1171349,1180021,1182194,1364953,1374313,1563341,1568345,1573357,1780517,1783186,1785857
%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 the two central terms are both 86.
%t cfo86Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{0,0}, ContinuedFraction[ s][[2]]];len=Length[cf];OddQ[len]&&cf[[(len+1)/2]] == 86]; Select[Range[1800000],cfo86Q] (* _Harvey P. Dale_, Jul 31 2013 *)
%K nonn
%O 1,1
%A _David W. Wilson_
%E Corrected and extended by _Harvey P. Dale_, Jul 31 2013