Collatz Problem

Define the following function on $\mathbb{N}$ : $f(n)=\begin{cases} 3n+1 & 2\nmid n, \\ \frac{n}{2} & 2\mid n.\end{cases}$ The Collatz conjecture say that, for any positive integer $n$ , the sequence $\{n,f(n),f(f(n)),f(f(f(n))),\ldots\}$ contains 1. This conjecture is still open. Some people have described it as the easiest unsolved problem in mathematics.