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%I #7 Mar 30 2012 18:39:17
%S 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,
%T 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,
%U 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
%N Number of steps needed to reach an integer starting with n+1/8 and iterating the map x-->x*ceiling(x).
%C 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.
%F It seems that sum(k=1, n, a(k)) is asymptotic to 4n.
%o (PARI) a(n)=if(n<0,0,s=n+1/8; c=0; while(frac(s)>0,s=s*ceil(s); c++); c)
%Y Cf. A068119, A073524.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Apr 13 2003
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