Kapitel 134: Chapter 127: Is this... Eunuch?

One day in 1976, the front-page headline of the "Washington Post" reported a piece of mathematical news.

The story unfolded as follows: In the mid-70s, campuses of prestigious universities in the United States saw people engrossed in a mathematical game as if they were possessed, working day and night, forsaking rest and meals. The game was incredibly simple: Write down any natural number N (N ≠ 0) and transform it according to the following rules:

If N is an odd number, the next step is 3N + 1.

If N is an even number, the next step is N/2.

Not only students, but even teachers, researchers, professors, and scholars joined the frenzy.

Why did this game have such enduring appeal? Because people discovered that no matter what non-zero natural number N was, it ultimately couldn't escape the descent into 1. To be precise, it couldn't escape falling into a 4-2-1 cycle, forever destined to this fate.