Does the series formed by adding a number to its reversal always end in a palindrome?

arithmetic/digits/palindrome Added material

Problem

Does the series formed by adding a number to its reversal always end in
a palindrome?

Show solution

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.

Additional material

Is that all that the archive says about other bases?  It's been known
for many years that the statement is false in any base which is a
power of 2: If you start with 30330 in base 4, or 70770 in base 8, or
F0FF0 in base 16, etc., then you can easily find the pattern of digits
in the successive sums and show that none are palindromes.  (If I
recall correctly, in base 2^n, there's a cycle of length 2n+2 during
which the lengths of the numbers increase by 2 digits.)

-- Dean Hickerson <dean@MATH.Ucdavis.EDU>

A shell script for Unix that uses 'dc' and 'rev' to find long-ish
number palindromes [ Editor: the script is omitted ] tells me

        89 becomes 8813200023188 after 24 steps

-- Felix Lee <flee@cse.psu.edu>