Take any positive whole number. If it is odd, multiply it by 3 and add 1. If it is even, divide it by 2.
Now repeat with the result. The resulting sequence of numbers will always end with ...4, 2, 1 (repeating).
This is known as the Collatz Conjecture
named after the German Mathematician Lothar Collatz.
Numbers which require increasing amounts of steps before settling down to ...4, 2, 1:
1, 2, 3, 6, 7, 9, 18, 25, 27, 54, 73, 97, 129, 171, 231, 313, 327, 649, 703, 871, 1161, 2223, 2463, 2919, 3711, 6171, ...
(sequence A006877 in the OEIS).
Perhaps interesting to know is that the Collatz Conjecture has not (yet) been proven or disproven.
For a really nice video on this, see Veritasium.