OFFSET
1,1
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.
FORMULA
It seems that sum(k=1, n, a(k)) is asymptotic to 5n.
MATHEMATICA
Table[Length[NestWhileList[# Ceiling[#]&, n+1/16, !IntegerQ[#]&]]-1, {n, 110}] (* Harvey P. Dale, Apr 02 2012 *)
PROG
(PARI) a(n)=if(n<0, 0, s=n+1/16; c=0; while(frac(s)>0, s=s*ceil(s); c++); c)
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 13 2003
STATUS
approved