3n+1

Here's a nice one called "3n+1" sequence. Take a random number and do
the following:
- if it is even, divide it by 2
- if it is uneven multiply it by 3 and add 1
Do this repeatedly and you'll always get to "1"

 The funny part is that there is no absolute proof for this rule, but
no-one has disproved it either. So far, each value taken as a start
value will end up being 1 in the end. Of course, the trick here is that
if you multiply an uneven number with 3 it will remain uneven. Add one,
it'll be even. So the final sequence will always be:
40-20-10-5-16-8-4-2-1 ... or does it?

 So, here's a try:
136 -> 68 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 ->
8 -> 4 -> 2 -> 1

 More interesting math: http://mathworld.wolfram.com/