Collatz recursion/Sequence/Definition

Collatz recursion

By Collatz recursion, we understand the following procedure to construct from a given natural number ${}k$ a new number.

If ${}k$ is even, then take the half of ${}k$.

If ${}k$ is odd, then multiply ${}k$ with ${}3$ and add ${}1$.

The Collatz sequence for the initial value ${}m$ is the sequence of numbers arising by applying the Collatz recursion to ${}m$ recursively.