Collatz conjecture

Collatz sequence, if nothing else, is an interesting thing.

The clever German mathematician, Collatz, all of a sudden thought that any positive integer number, would create a sequence ending with 1 (or alternatively entering the 4-2-1-4 loop) when the following partial function is applied to it.

collatzSequence x
    | x <= 1 = [1]
    | even x = x : collatzSequence (div x 2)
    | odd  x = x : collatzSequence (3*x+1)

[ This is valid Haskell code by the way ]


And Collatz was right, most probably. That's not for sure since no proof for it exists, but using quite a lot of computing power a counter-example couldn't be found. So the question of whether Collatz was right or not stands as an open problem.


I, humbly, did some experiments and tried to have an idea looking at the lengths of such sequences. In addition to the analysis of lengths I had also tried to plot the sequences and investigate where sequences for consequent numbers catch up.
It was at least 3 (or 4?) years ago. And now that I present a more scientific profile, I thought I might come up with some more clever points. Initial results are *NOT* promising, but I'll keep on thinking.