This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A081885 #10 Nov 21 2013 12:48:00
%S A081885 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 A081885 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 A081885 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 A081885 Number of steps needed to reach an integer starting with n+1/16 and iterating the map x-->x*ceiling(x).
%C A081885 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 A081885 It seems that sum(k=1, n, a(k)) is asymptotic to 5n.
%t A081885 Table[Length[NestWhileList[# Ceiling[#]&,n+1/16,!IntegerQ[#]&]]-1, {n,110}] (* _Harvey P. Dale_, Apr 02 2012 *)
%o A081885 (PARI) a(n)=if(n<0,0,s=n+1/16; c=0; while(frac(s)>0,s=s*ceil(s); c++); c)
%Y A081885 Cf. A068119, A073524.
%K A081885 nonn
%O A081885 1,1
%A A081885 _Benoit Cloitre_, Apr 13 2003