It is easy, we can spit it into two parts: Proving that all even numbers end up in that loop and proving that all odd numbers do.
I'll take the even ones. Who works on the odd ones?
I'll take the even ones. Who works on the odd ones?
An odd number is a number that ends in 1, 3, 5, 7, or 9.
- ends in a 1: times 3 + 1: it now ends in a 4, which is even, and thus reduces to the even case.
- ends in a 3: tomes 3 is 9, + 1: ends in a 0; even again.
- ends in a 5: ×3 ends in a 5 again, +1: ends in a 6; again even!
- ends in 7: x3: now ends in a 1, +1: ends in a 2; even yet again!
- ends in a 9: ×3 then eens in a 7, +1 thus eens in an 8: even again!!
So all that's left is the cases for @someweirdperson ;-) @someweirdperson
This approach, like every other approaches, did not yield any significant result.
The funny thing is that it fits right in the P=NP problem: easy to verify, hard to solve :)