Halve it, or triple it and add 1

Pick any number. Follow two rules. See what number you reach.

The rule

If the number is even, halve it: divide it by 2. If it is odd, multiply it by 3 and add 1. Repeat until you reach 1.

This is the Collatz process. The list of numbers you get is the sequence.

Example

Start with 6. 6 is even: 6 ÷ 2 = 3. 3 is odd: 3 × 3 + 1 = 10. 10 is even: 10 ÷ 2 = 5.

The whole sequence:

6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1.

That is 8 steps. 100 takes 25 steps.

People have checked very many starting numbers. All reached 1. No one has proved this for every number.

Try the lab to finish this lesson.