So there is this weird phenomenon that occurs when you follow these specific rules:
If ODD 3x+1
If EVEN x/2
The theory is that if you take a number through these rules as far as possible you will achieve a never ending cycle of 4,2,1. So say for instance you start with 5 follow the ODD function to get 16 then even function for 8 again for 4 again for 2 again for 1 then 4, 2, 1, 4, 2, 1... As far as I am aware this has not been proven to work for every number and it is unsure if there could be other sequences like this that appear from numbers untried. I guess my point is for a discussion to see if it can't be proven.