It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any natural number, apply f, then apply f again and again. You eventually land on 1, for every number we’ve ever checked. The Conjecture is that this is true for all natural numbers.
P.S. This problem has never been fully solved, but a great attempt was made by: Terence Tao.
n+1 if odd would give that f^2(n) is always less than or equal to f(n), thus providing a simple proof that every sequence will eventually become ... 1, 2, 1, 2, 1, 2, ...
I usually see this conjecture called the "3n+1 conjecture."
P.S. This problem has never been fully solved, but a great attempt was made by: Terence Tao.
Mathematicians are so close! https://www.popularmechanics.com/science/math/a29033918/math-riddle-collatz-conjecture/