A081885 - OEIS

%I #10 Nov 21 2013 12:48:00

%S 8,5,3,8,18,8,5,6,5,6,3,6,7,5,1,6,4,6,3,4,2,6,2,7,3,2,4,6,2,5,1,8,12,

%T 4,7,4,8,7,3,9,10,5,3,9,5,6,1,3,11,4,2,4,4,4,2,4,6,7,2,2,5,3,1,7,9,9,

%U 5,7,4,13,4,5,6,8,6,14,8,3,1,4,2,5,4,5,3,2,2,10,2,5,3,18,4,3,1,11,4,7,7,4,5

%N Number of steps needed to reach an integer starting with n+1/16 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 5n.

%t Table[Length[NestWhileList[# Ceiling[#]&,n+1/16,!IntegerQ[#]&]]-1, {n,110}] (* _Harvey P. Dale_, Apr 02 2012 *)

%o (PARI) a(n)=if(n<0,0,s=n+1/16; 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