Collatz: does every number reach 1?
The rule: if a number is even, halve it. If it is odd, triple it and add 1. Repeat. Type a starting number and watch where it goes.
Your number
Type a number above, or tap an example.
Show every value
The path
Each point is one step. The line ends at 1.
Record starts
Which start under a limit takes the most steps, and which climbs highest? The page checks every start, right now.
Working...
What is known
This is the Collatz conjecture, posed by Lothar Collatz in 1937. It says every whole number above zero ends at 1. Nobody has proved it, and nobody has found a number that fails. This page cannot settle it either: it only shows the steps for the numbers you try.
A step is one use of the rule, so 1 takes 0 steps and 2 takes 1. The highest value counts the starting number too. Your number is worked out with exact whole-number arithmetic, so 30-digit numbers are not rounded. Nothing you type is sent or kept.