# Definition:Collatz Sequence

## Definition

Let $f: \N \to \N$ be the mapping defined on the natural numbers as follows:

$\forall n \in \N: \map f n = \begin{cases} n / 2 & : n \text { even} \\ 3 n + 1 & : n \text { odd} \end{cases}$

For any given value of $n$, let the sequence $\sequence {S_k}$ be defined:

$\forall k \in \N: S_k = \begin {cases} n & : k = 0 \\ \map f {S_{k - 1} } & : k > 0 \end {cases}$

Then $\sequence {S_k}$ is known as a Collatz sequence.

## Source of Name

This entry was named for Lothar Collatz.