A072899 Denominator of c(n) where c(0)=1 c(n+1) = n/c(n) + 1.

1, 1, 1, 1, 2, 5, 13, 19, 58, 191, 655, 1187, 4462, 17519, 71063, 149405, 646846, 2887921, 13237457, 31166057, 150303170, 742458253, 3748521653, 9670072483, 50903810666, 273315477775, 1495006933759, 4163946939067, 23599037077934

Offset

0,5

Comments

Dvornicich et al proved that c(n) is an integer only for n<4, so that a(n)=1 only for n<4. - Michel Marcus, Dec 24 2020

Links

Table of n, a(n) for n=0..28.

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....

Mathematica

Denominator[RecurrenceTable[{c[1]==1, c[n]==(n-1)/c[n-1]+1}, c, {n, 30}]] (* Harvey P. Dale, Jun 11 2013 *)

Prog

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

Crossrefs

Cf. A072898.

Sequence in context: A068374 A068371 A327909 * A099982 A298991 A046696

Adjacent sequences: A072896 A072897 A072898 * A072900 A072901 A072902

Keyword

easy,frac,nonn

Author

Benoit Cloitre, Aug 10 2002

Extensions

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

Status

approved