Palindromes

For some integers a palindrome can be created by reversing the digits and adding the new number to the original number e.g.: 31+11=44. a palindrome. if the first step doesn't produce a palindrome then do the same thing again and again till you get a palindrome.
e.g. 157 + 751=908
908 + 809=1717
1717 + 7171=8888 - a palindrome!

Can this be done for all integers? I think not cos for larger numbers the size of the palindrome could be enormous. opinions?

tl,dr

>>1
No one knows if the method produces a palindromic number for all integers.  It’s a well known unsolved problem in number theory:

http://mathworld.wolfram.com/196-Algorithm.html

>>1
More like 31+13=44. Yeah, awesome method, fails hard for 196 and others, no one knows why, big mistery.

Spoiler: The palindrome rule used depends on the decimal system.