The problem is that the numbers can go up and go down.
To prove that the conjecture is not true is to find a number that as you do the sequence, the sequence return to the original number. That would be an infinite loop, as it would never go to zero, but constantly repeat the pattern. In addition, every number in this sequence would not lead to 1.
A clearer understanding of the problem.
Any ideas for reading material here?
The Idiots Guide to Theoretical Mathematics?