There's a lot of number sequence based questions on this site. So I'm going to mix it up a little bit. This sequence will repeat eventually. You need to find how many numbers are in the sequence before it starts repeating. (Still give reasoning for your answer, however.)
Before you OEIS this, I've already done it. Doesn't work.
13, 16, 25, 62, 84...
(Edit: Sequence has been fixed, whoops! Still not OEIS-able.)