A072898 Numerator of c(n) where c(0)=1, c(n+1) = n/c(n) + 1.

1, 1, 2, 2, 5, 13, 38, 58, 191, 655, 2374, 4462, 17519, 71063, 298810, 646846, 2887921, 13237457, 62332114, 150303170, 742458253, 3748521653, 19340144966, 50903810666, 273315477775, 1495006933759, 8327893878134, 23599037077934

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Roberto Dvornicich, Francesco Veneziano, and Umberto Zannier, On the integral values of a curious recurrence, arXiv:1403.3470 [math.NT], 2014.

Index to sequences related to Olympiads.

Formula

It seems that log(a(n)) is asymptotic to C*n*Log(n) with C=0.4....

Prog

(PARI) lista(nn) = {my(x = 1); for (n=0, nn, print1(numerator(x), ", "); x = 1+ n/x; ); } \\ Michel Marcus, Dec 24 2020

Crossrefs

Cf. A072899.

Sequence in context: A019083 A355863 A029856 * A032290 A032201 A268180

Adjacent sequences: A072895 A072896 A072897 * A072899 A072900 A072901

Keyword

easy,frac,nonn

Author

Benoit Cloitre, Aug 10 2002

Extensions

a(0)=1 prepended by Michel Marcus, Dec 24 2020

Status

approved