I was doing some research into the Collatz conjecture and the main problem as I see it is this: What does +1 do to a factorization?
Is there any patterns, theorems or recent research that tackles this question: How does adding one affect factorization?
What I though maybe easier (or much harder, who knows) since it is a more specific case directly relating to the Collatz: $3/2x+1/2$ how does that change the factorization of x for odd x.