I can prove that for any positive $\mathbb{Z+}$ the conjecture will always converge to 4 hence entering the loop. $$ 4 \to 2 \to 1 \to 4 \to ... $$ To do this I used the formula of odd number and even number as follows: $$odd = 2x + 1$$ $$even = 2x$$ The rule says: $$odd \to 3x + 1$$ $$even \to \...

This question is purely out of interest and curiosity. The Collatz Conjecture is as follows: Consider any positive whole number $n$ and apply two procedures to it. If $n$ is odd, then n becomes $ 3n + 1 $. If $n$ is even, then $n$ becomes $\frac{n}{2}$. Infinitely repeating that procedure will ...