Collatz Trails
Take a whole number. If it is even, halve it. If it is odd, triple it and add one. Repeat. Every number tried so far ends at 1. Nobody has proved that all of them do; that is the Collatz conjecture, posed by Lothar Collatz in 1937. This page counts the steps for every number up to a limit you choose, and draws the path of any one of them.
Steps to reach 1, for every n
Each dot is one number. Orange dots are record holders: numbers that take more steps than every smaller number. Click the plot to choose a number.
The path of the chosen number
Bar heights are on a log scale, so small and very large values both show. The tallest bar is the peak.
Record holders
Numbers checked:
Mean steps:
Most steps:
| n | Steps | Peak value |
|---|