Well, no, it's O(n), I was trying to make a mathematical point, not a complexity one...
QuantumPete
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It's not O(n) either, you can't know how the algorithm will behave, for now, all i know is that if n is a power of 2, the complexity will be O(log2(n))
I'm coding something right now to analyze it.
EDIT: here, look at the complexity plot of the 3n+1 problem
http://img258.imageshack.us/img258/5613/plotpv7.jpg
The average iteration number from 1 to 256 is 44.98046875.