Re: [math-fun] Add 1 and reverse

On 30/09/2015 15:29, Warren D Smith wrote:

OK, the Mitchell/Smith/McCaughan theorem now shows when w=odd that X := reverse(X+1) (all mod 2^w) has period=2^w, and when w=even we get period=2*2^(w/2)-1.

Careful! In the even case there are lots of orbits with different periods. That particular period is only for the orbit containing 0. (This has no impact, I think, on your very interesting conjectures about the generalized iteration.) -- g