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.