Haha! My math is so weak, I needed to ask...chat is really lazy. Didn't even try, the first line "nobody knows" says it all.

SimpleStacker

There is no known proof that every positive integer eventually reaches the 4→2→14 \to 2 \to 1 loop, and no counterexample has ever been found.

f(n)={n/2n even3n+1n oddf(n)= \begin{cases} n/2 & n\text{ even}\ 3n+1 & n\text{ odd} \end{cases}

Starting from every positive integer, repeated application of this rule eventually reaches 1.

3→10→5→16→8→4→2→1→4→2→1…3\to10\to5\to16\to8\to4\to2\to1\to4\to2\to1\ldots

Despite enormous computational verification, 

a general mathematical proof remains an open problem

So the 700,000-sat bounty is essentially asking someone to solve one of mathematics' famous unsolved problems—or produce the first genuine counterexample.

 to always enter the 4,2,14,2,1 loop, but this has not been proven.

math

[Math Puzzle] Does every sequence terminate in a loop?

mathGPT  answers! 


**Nobody currently knows.** 

There is no known proof that every positive integer eventually reaches the 4→2→14 \to 2 \to 1 loop, and no counterexample has ever been found.

The rule is:

f(n)={n/2n even3n+1n oddf(n)= \begin{cases} n/2 & n\text{ even}\\ 3n+1 & n\text{ odd} \end{cases}

The conjecture states:

> **Starting from every positive integer, repeated application of this rule eventually reaches 1.**

For example:

3→10→5→16→8→4→2→1→4→2→1…3\to10\to5\to16\to8\to4\to2\to1\to4\to2\to1\ldots

Despite enormous computational verification, **a general mathematical proof remains an open problem**.

So the 700,000-sat bounty is essentially asking someone to solve one of mathematics' famous unsolved problems—or produce the first genuine counterexample.

**Bottom line: the sequence is *conjectured* to always enter the 4,2,14,2,1 loop, but this has not been proven.**