Palindrome Root

Computer Science Level pending

Most of the positive integers can form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. For example, for the number 19,

\[\begin{aligned} 19 + 91 &= 110 \\ 110+011 &= 121\end{aligned}\]

can form the palindrome 121 after 2 iterations. In this case, we call 19 the root of palindrome 121. A number \(n\) is the root of palindrome \(p\) if it is the smallest number such that after going through some number of iterations the first palindrome it forms is \(p\).

What is the root of the following number?



Although 7 can form 121 after some number of iterations, it is not the root of 121 because the first palindrome formed by it is 55.


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