Going into this completely blind and uneducated on what the Collatz conjecture is.

Trying to prove the sequence always hits the repeating (4,2,1) seems like an incredible undertaking, and I don't even know where I would start.

Instead I will try and disprove it. The idea is finding a number that gets stuck in repeated odd results, in order to expand indefinitely.

I first tried x
Where x is a prime #, and x != 1, 2, 3 or 5.
This is silly in hindsight because 29 is prime and results in the same loop, but the math demonstrates the issue I ran into repeatedly with my different approaches of trying to make a number repeatedly come out odd.

based on the above definition of x:
x is odd

3x + 1 = odd*odd + 1 = odd + 1 = even

I will skip the proof for odd*odd = odd, it is well known.

Because the result is now even:

(3x + 1)/2 = 3x/2 + 1/2 = odd*odd/2 + 1/2 = odd/2 + 1/2

Odd #s are 2n + 1, so

(2n + 1)/2 + 1/2 = n + 1

Unfortunately I don't think I have any way of determining if n is even or odd so I am stuck.

Based on what I am reading in this thread it sounds like my results were expected.

I'm hopping this apeases my curiosity and I can get back to work and not try and prove everything reaches the 421 loop lol.