Unproven fact(?)

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Select any positive integer.

For example, if this operation is performed on 3, the result is 10; if it is performed on 28, the result is 14.

Now consider that you perform this operation repeatedly, where the result is used as the new number.

So, if you start with 6, you get the sequence 6, 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1,...

It seems that no matter what number we start with, we always eventually get stuck in the loop: 4, 2, 1, 4, 2, 1, etc.

Try it!

As far as I know this has not been proven, but it has been tested for all start values up to 13 258, but this might have increased by the time you read this.

This is called the "Collatz conjecture", "roller-coaster sequence", and the "Syracuse problem". You can read more about it here