cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A065098 Sum of reciprocals of terms in period of continued fraction for sqrt(n) is an integer.

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%I A065098 #4 Apr 11 2016 17:17:58
%S A065098 239,1839,24627
%N A065098 Sum of reciprocals of terms in period of continued fraction for sqrt(n) is an integer.
%C A065098 No additional terms up to n = 1 million. - _Harvey P. Dale_, Apr 11 2016
%e A065098 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 A065098 Do[ If[ IntegerQ[ Apply[ Plus, 1/Last[ ContinuedFraction[ Sqrt[n]]]]], Print[n]], {n, 2, 10^5 } ]
%t A065098 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 A065098 Cf. A003285, A010340.
%K A065098 nonn,bref
%O A065098 1,1
%A A065098 _Naohiro Nomoto_, Nov 12 2001