Is it possible, using the Collatz hailstone sequence to ever start at a number n and end up with 2n at some point later in the sequence for values greater than 2? Can you have a sequence that goes n . . . 2n (I don't care what any of the exact values are, I want to know if using variables it is...
Would it be possible to prove the collatz conjecture indirectly by demonstrating rules that apply to 'Collatz-like' conjectures? (I call anything where you simply change the values in the 3n+1 part of the conjecture to other values, holding everything else the same a Collatz-like conjecture)...