For the last year or so I've been thinking about what seems to be a fairly obscure number-theoretic problem. I'll do my best to describe it here.
This problem is all about the reverse-and-add algorithm. I.e., you reverse an integer's digits (in a certain base) and add it to itself over and over. The sequence, if it terminates, ends when the digits of the sum are palindromic. Palindromic numbers are the same forwards and backwards, for example: 696, 133312213331, 33, 121, 0xBEEFEEB, etc.
Here's what that looks like for the number 48 (in base 10):