From: saouter@poseidon.irit.fr (Yannick SAOUTER) Newsgroups: sci.math Subject: Re: Number Theory and 3*n+1 Date: 19 Jan 1998 09:33:21 GMT In article <34C25C44.21F5@fremont.vegasnet.org>, Troy Kessler writes: |> Has anyone tried to change the 3*n+1 conjecture to a 5*n+1 conjecture or |> a o*n+1 conjecture where o is odd? Which odd numbers seem to work? There is the Crandall's conjecture which states that the iteration: qx+1 when x odd x/2 when x even has always divergent cycle when q is odd and greater than 3. It has been proved by Carl Pomerance (if I do not mistake) that this is true for so-called Wieferich's numbers whose measure is aymptotically 1. It appears in Math. Comp. However, except this result, I do not know of non trivial result deciding of convergence or divergence of such or such Conway-like iteration. Is there any ? Yannick Saouter.