I have an integer (in decimal representation) such that if I reverse its digits and add them up, I will get a new integer. I repeat this process until the resulting integer is a palindrome. We will denote an integer as a near-symmetric number if after twenty-five iterations, the resulting integer is still not a palindrome. What is the smallest positive near-symmetric number?
Details and assumptions
A palindrome is a number that remains the same when its digits are reversed.
As an explicit example, consider the integer to be . The resulting number will be . Repeat: , which is a palindrome (after iterations). Thus is not a near-symmetric number.