

A065098


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


0




OFFSET

1,1


COMMENTS

No additional terms up to n = 1 million.  Harvey P. Dale, Apr 11 2016


LINKS

Table of n, a(n) for n=1..3.


EXAMPLE

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.


MATHEMATICA

Do[ If[ IntegerQ[ Apply[ Plus, 1/Last[ ContinuedFraction[ Sqrt[n]]]]], Print[n]], {n, 2, 10^5 } ]
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 *)


CROSSREFS

Cf. A003285, A010340.
Sequence in context: A201787 A118574 A142854 * A256378 A256377 A177204
Adjacent sequences: A065095 A065096 A065097 * A065099 A065100 A065101


KEYWORD

nonn,bref


AUTHOR

Naohiro Nomoto, Nov 12 2001


STATUS

approved



