Tomás Oliveira e Silva of the Universidade de Aveiro, in Portugal, apparently. According to a page on his personal website [http://sweet.ua.pt/tos/3x+1.html] he has verified it up to 5 x 2^60.
I just implemented it too. I notice that by 100K, you get an intermediate result of size just less than 2^31, but at 1M, you get an intermediate result of size about 2^36. Maybe I went up above 100K.
For more: http://en.wikipedia.org/wiki/Collatz_conjecture#Experimental..., which includes some very nice plots, and a fractal construction when iterating an extension of the map to the complex plane. Whew! (On the other hand, https://xkcd.com/710/)
It needs to land on a power of 2 at some point.
No one knows.
> Is there a name for this problem?
The statement that it always terminates is the Collatz Conjecture. It's the first problem in the posted article.
It's a clever way to re-state the problem to look more computer-science-y.
There are heuristic to show that the algorithm should terminate but there are numbers for which it takes an arbitrarily long time for convergence. Furthermore, there are similar problems that have divergence or loops. What makes matters worse is that it's been proven that such problems are undecidable in general.
The problem was posed as a while loop, and the question was, does the loop terminate for arbitrary n>0, so it seemed very tractable:
It was a tease. I tried a couple of different ways to prove it, but of course nothing worked. Then I tried to find a counter-example. The numbers get pretty big, in some cases, because applying several times in a row will blow "n" up, despite the intervening n = n/2. This was before arbitrary-precision arithmetic was a thing, so the only tool I knew that could do this was the Unix "dc". I think I was able to get up to n=10K or 50K on our campus VAX.That was about 30 years ago. I still remember it fondly.