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 A081884 #7 Mar 30 2012 18:39:17 %S A081884 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 A081884 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 A081884 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 A081884 Number of steps needed to reach an integer starting with n+1/8 and iterating the map x-->x*ceiling(x). %C A081884 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 A081884 It seems that sum(k=1, n, a(k)) is asymptotic to 4n. %o A081884 (PARI) a(n)=if(n<0,0,s=n+1/8; c=0; while(frac(s)>0,s=s*ceil(s); c++); c) %Y A081884 Cf. A068119, A073524. %K A081884 nonn %O A081884 1,1 %A A081884 _Benoit Cloitre_, Apr 13 2003