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

239, 1839, 24627

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: A289390 A118574 A142854 * A256378 A256377 A201194

Adjacent sequences: A065095 A065096 A065097 * A065099 A065100 A065101

Keyword

nonn,bref

Author

Naohiro Nomoto, Nov 12 2001

Status

approved