==> arithmetic/digits/palindrome.s <==
This is not known.

If you start with 196, after 9480000 iterations you get a 3924257-digit
non-palindromic number.  However, there is no known proof that you will
never get a palindrome.

The statement is provably false for binary numbers. Roland Sprague has
shown that 10110 starts a series that never goes palindromic.