The hailstone problem has been a repeated discussion topic at the weekly meetings. (With new and interesting observations about it sometimes presented)
So... probably there should be some explanation of what the problem is...
If you start with a positive integer, multiply it by three, add one to the result, and then remove all factors of two, you will get some result. It is observed that if you do this repeatedly you will eventually hit the result ONE. There is, however, neither a proof that the sequence MUST hit 1, nor is there a counterexample known. (Although empirically it is known that there is no counterexample less than 10 billion)
The problem has appeared in print numerous times (Apparently, for example, in the January 1984 issue of Scientific American). It is also frequently called the Collatz problem. A google search on "hailstone problem" gives a lot of sites on the topic.
It is currently known (as reported by http://mathworld.wolfram.com/CollatzProblem.html, which I take as a trustable source) that there are no counter examples less than 10,000,000,000,000,000
This page is http://web.utah.edu/utahlogic/misc/factoring.html This page was last modified on July 11th, 2004.