Collatz Conjecture

mathematics

Definition

Collatz Conjecture

The Collatz conjecture states that for every positive integer $x$, repeated application of the Collatz iteration eventually reaches $1$.

The iteration is defined by

$$x_{n+1}=\{\begin{array}{ll}{x}_n/2& \text{if }{x}_n\text{ is even}\\ 3x_n+1& \text{if }{x}_n\text{ is odd}\end{array}$$

It is an open problem whether this process terminates for all $x\ge 1$.