A proof has been suggested on Quora for "the nth terms of convergence of the Collatz map". (I am restarting this market as multiple choice, now Manifold has that option.)

There are two parts to the proof:

A general statement of the theorem, https://qr.ae/pyD8Nk, and an inductive proof of that theorem, https://qr.ae/pKRv1A. 

The ambiguity is whether or not proving convergence of the nth terms is the same as proving all sequence Ns converge on 1.

A third, generalized, proof may be published on Quora. 

If you want to learn about the conjecture and its place in contemporary mathematics, watch the Veritasium video on YouTube: https://youtu.be/094y1Z2wpJg

About the prize: https://mathprize.net/posts/collatz-conjecture/

Collatz conjecture Prize 120 million JPY

A prize of 120 million JPY will be paid to those who have revealed the truth of the Collatz conjecture. The conjecture is also known as the \(3x + 1\) problem or the \(3n + 1\) problem. 120 million JPY in USD Collatz conjecture Repeatedly applying the function \(f(x)\) defined below to any positive integers will eventually result in \(1\). \[ f(x) = \left \{ \begin{array} \\ x \mathbin{/} 2 & (x \equiv 0 \pmod 2) \\ 3 x + 1 & (x \equiv 1 \pmod 2) \end{array} \right. \]