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 A118020 #3 Mar 30 2012 17:22:42
%S A118020 0,-1,3,-1,12,2,3,-1,7,2,18,8,7,22,3,-1,6,8,17,-1,25,3,68,4,8,14,3,11,
%T A118020 171,6,19,5,11,11,16,6,23,19,6,-1,55,3,23,10,4,26,58,6,12,3,13,3,62,9,
%U A118020 9,4,19,62,105,9,7,24,7,-1,3,17,16,12,66,21,66,-1,63,65,6,28,20,20,54,-1,13,92,19,21,7,9,34,36,67,5,20,5,29,62,39,6,105
%N A118020 Number of steps to reach an integer starting with (n+1)/n and using the approximate cubing map x -> x*ceiling(x^2); or -1 if no integer is ever reached.
%C A118020 This sequence is similar to A073524, approximate squaring. However, for the cubing map it is easy to show that fractions of the form odd/2 never yield an integer. Hence if an iterate ever has this form, then we know it will never yield an integer. The computations, similar to A073524, must be done modulo n^max for some max > 2*a(n)+2.
%e A118020 a(3)=3 because 4/3 -> 8/3 -> 64/3 -> 9728.
%t A118020 Stuck[x_] := OddQ[Numerator[x]] && (Denominator[x]==2); Table[lim=50; While[k=0; x=1+1/n; m=n^lim; While[2k<lim-3 && !IntegerQ[x] && !Stuck[x], x=Mod[x*Ceiling[x^2],m]; k++ ]; 2k>=lim-3, lim=2*lim]; If[Stuck[x],-1,k], {n,200}]
%Y A118020 Cf. A118021 (n for which a(n)=-1).
%K A118020 sign
%O A118020 1,3
%A A118020 _T. D. Noe_, Apr 10 2006