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%I #4 Apr 11 2016 17:17:58
%S 239,1839,24627
%N Sum of reciprocals of terms in period of continued fraction for sqrt(n) is an integer.
%C No additional terms up to n = 1 million. - _Harvey P. Dale_, Apr 11 2016
%e For n=239 the quotient periods are: [[15],[2,5,1,2,4,15,4,2,1,5,2,30]], (1/2)+(1/5)+1+(1/2)+(1/4)+(1/15)+(1/4)+(1/2)+1+(1/5)+(1/2)+(1/30) = 5.
%t Do[ If[ IntegerQ[ Apply[ Plus, 1/Last[ ContinuedFraction[ Sqrt[n]]]]], Print[n]], {n, 2, 10^5 } ]
%t srcfiQ[n_]:=Module[{s=Sqrt[n]},IntegerQ[If[IntegerQ[s],1/2,Total[1/ ContinuedFraction[s][[2]]]]]]; Select[Range[25000],srcfiQ] (* _Harvey P. Dale_, Apr 11 2016 *)
%Y Cf. A003285, A010340.
%K nonn,bref
%O 1,1
%A _Naohiro Nomoto_, Nov 12 2001