A081884 Number of steps needed to reach an integer starting with n+1/8 and iterating the map x-->x*ceiling(x).

4, 7, 4, 7, 7, 6, 1, 3, 2, 2, 2, 7, 2, 3, 1, 6, 5, 4, 3, 7, 7, 6, 1, 3, 3, 5, 2, 2, 3, 3, 1, 5, 3, 9, 6, 4, 7, 3, 1, 3, 2, 3, 2, 3, 2, 2, 1, 5, 5, 4, 3, 10, 3, 4, 1, 2, 4, 5, 2, 7, 7, 9, 1, 6, 6, 3, 4, 12, 3, 13, 1, 5, 2, 2, 2, 10, 2, 5, 1, 5, 3, 13, 3, 3, 5, 6, 1, 9, 3, 6, 2, 2, 3, 4, 1, 6, 6, 6, 5, 6, 4, 4, 1

Offset: 1

Author

Benoit Cloitre, Apr 13 2003

Keywords

• nonn

Comments

Conjecture : let b(n,m) denotes the number of steps needed to reach an integer starting with n+1/2^m and iterating the map x-->x*ceiling(x); then sum(k=1,n,b(k,m)) is asymptotic to (m+1)*n.

Crossrefs

Cf. A068119, A073524.

Programs

PARI

a(n)=if(n<0,0,s=n+1/8; c=0; while(frac(s)>0,s=s*ceil(s); c++); c)

Formula

It seems that sum(k=1, n, a(k)) is asymptotic to 4n.