I'm not mathematician, so forgive me if I make wrong assumptions. I was wondering what the importance of the $3n$ is in the Collatz Conjuncture.
If you just do $n + 1$, it seems you'll end up at $1$ also.
This would seem logical to me, because you'll do $n + 1$ when it's an uneven number. The effect is that now you've made it an even number. Any you'll be able to reduce any even number to $2$ (possible wrong assumption here?). And $\frac{2}{2}$ is $1$.
So instead of:
$\quad$ Even number: $\frac{n}{2}$
$\quad$ Uneven number: $3n + 1$
Couldn't it be:
$\quad$ Even number: $\frac{n}{2}$
$\quad$ Uneven number: $n + 1$
Or has someone else already answered this question? Again, I'm no mathematician, so not really familiar with this.