A071647 a(n) is the maximum number of elements among the continued fractions for n/1, n/2, n/3, n/4, ..., n/n.

1, 1, 2, 2, 3, 2, 3, 4, 3, 3, 4, 4, 5, 4, 4, 4, 4, 5, 5, 4, 6, 4, 5, 4, 5, 5, 5, 5, 6, 6, 6, 5, 5, 7, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 7, 7, 6, 6, 6, 5, 8, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 7, 7, 7, 7, 6, 7, 6, 7, 7, 7, 8, 6, 6, 8, 8, 8, 7, 7, 6, 7, 7, 7

Offset

1,3

Comments

a(n)/log(n) is bounded.

Apart from initial term, same as A034883. - Franklin T. Adams-Watters, Nov 14 2006

Links

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Example

Continued fractions for 5/1 = [5]; 5/2 = [2, 2]; 5/3 = [1, 1, 2]; 5/4 = [1, 4]; 5/5 = [1] hence a(5) = 3.

Prog

(PARI) for(n=1, 150, print1( vecmax(vector(n, i, length(contfrac(n/i)))), ", "))

Crossrefs

Cf. A034883.

Sequence in context: A238943 A070081 A366686 * A034883 A338643 A051125

Adjacent sequences: A071644 A071645 A071646 * A071648 A071649 A071650

Keyword

nonn,easy

Author

Benoit Cloitre, Jun 22 2002

Status

approved