# Collatz problem

• posted

I was looking at this for fun today and noticed probably something that is completely obviously but I just wanted to run it by you guys and see whats going on about it.

Basicaly the "tail" of one sequence always seems to end up being another sequence.

I've did some simulations and it seems that I can always find a b such that the sequence of b is exactly the same as the sequence of a except with a attached to b.

i.e.,

if a> = is the a vector of the elements generated by the collatz map then there seems to exist an b such that b> = . (i.e., b_i = a_(i-1)).

Not sure if this is always the case but has worked for several that I have tested. It would seem that if this is true one could always get to 1 because you could find a chain of integers that would be descending in size... in essense it would be equivilent to building up the integers by using the "inverse" collatz map and you could get them all.

Just curious. Probably would be just has hard to prove as the original problem.

Thanks, Jon