The Collatz function is the D4949: Natural number function $$\begin{equation} \mathbb{N} + 1 \to \mathbb{N} + 1, \quad n \mapsto \begin{cases} 3 n + 1, \quad & n \in 2 \mathbb{N} + 1 \\ n / 2, \quad & n \in 2 \mathbb{N} \end{cases} \end{equation}$$

The Collatz function is the D4949: Natural number function $$\begin{equation} \{ 1, 2, 3, \ldots \} \to \{ 1, 2, 3, \ldots \}, \quad n \mapsto \begin{cases} 3 n + 1, \quad & n \in \{ 1, 3, 5, \ldots \} \\ n / 2, \quad & n \in \{ 0, 2, 4, \ldots \} \end{cases} \end{equation}$$