Enigma 1117: Reapply as necessary
From New Scientist #2273, 13th January 2001 [link]
Recently I read this exercise in a school book:
“Start with a whole number, reverse it and then add the two together to get a new number. Repeat the process until you have a palindrome. For example, starting with 263 gives:
leading to the palindrome 2662.”
I tried this by starting with a three-figure number. I reversed it to give a larger number, and then I added the two together, but my answer was still not palindromic. So I repeated the process, which gave me another three-figure number which was still not palindromic. In fact I had to repeat the process twice more before I reached a palindrome.
What number did I start with?