Hailstone Numbers
If a number is even, halve it; if odd, triple it and add one. Repeat, and every number seems to come back to 1. See the journey as a graph.
Following the numbers…
27 → 82 → 41 → 124 → 62 → 31 → 94 → 47 → 142 → 71 → …
How to play
Type a number and press "Go", or tap one of the numbers below. If the number is even it is halved; if odd it is tripled and increased by one. This repeats until it reaches 1, and the values are drawn as a graph. You can use whole numbers from 1 to 99999.
Learn more
The guess that every starting number comes back to 1 is called the Collatz conjecture. Computers have checked a huge number of starting values and found none that fail. But nobody has proved that it holds for every number. It is an unsolved problem in mathematics. For example, 27 climbs up to 9232 before it comes back to 1 after 111 steps. Among starting numbers below 1000, 871 takes the most steps: 178.