# COLLATZ TREE

## BY ROLF TIMMERMANS •

This tree is based on the “Collatz sequence”: given any positive integer number **n** we can define the next number **n′** in the sequence with:

- If
**n**is even, then**n′ = n / 2**. - If
**n**is odd, then**n′ = 3n + 1**.

In 1937 Lothar Collatz proposed that no matter the initial value of **n**, the sequence will always reach 1. This conjecture is (perhaps surprisingly) still unproven, although it is generally believed to be true.

The tree is built from all sequences with all numbers below 9200. The trunk of the tree corresponds to 1.