Many Paths of the Collatz Conjecture

The Collatz Conjecture is one of mathematics' strange unsolved problems. The rule is deceptively simple: take any positive integer, and if it's even divide it by 2, if it's odd multiply by 3 and add 1. Repeat this process and the sequence seems to always eventually reach 1. Always. This is true for every number ever tested! Even still, no one has ever been able to prove it, though some attempts have got close.

The sequences themselves are practically unpredictable. For example, the number 27 takes 111 steps while rocketing up to 9,232 before finally collapsing to 1. Nearby numbers can reach 1 in just a handful of steps, while others take hundreds of chaotic steps before converging. Use the interactive math tool below to explore and compare up to 5 numbers at once.

Collatz Conjecture Visualizer

Pick any positive integer. If it's even, divide by 2. If it's odd, multiply by 3 and add 1. Repeat. No matter what number you start with, the sequence always seems to reach 1, but nobody has ever proved why. Enter up to 5 numbers to compare their paths.

Enter Numbers to Compare

About the Collatz Conjecture: Mathematician Paul Erdős said: “Mathematics is not yet ready for such problems.”

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