A081882 Number of steps needed to reach an integer starting with n-1/4 and iterating the map x ->x*ceiling(x).

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

Offset: 2

Author

Benoit Cloitre, Apr 13 2003

Keywords

• nonn

Crossrefs

Cf. A068119.

Programs

PARI

a(n)=if(n<0,0,s=n-1/4; c=0; while(frac(s)>0,s=s*ceil(s); c++); c)

Formula

It seems that sum(k=2, n, a(k)) is asymptotic to 3n