A Lychrel number is a natural number that is not known to form a palindrome through the iterative process of reversing its digits and adding the result to the original number. A number is considered a palindrome if it reads the same forwards and backwards (for example, 121 or 12321). The Lychrel process typically involves the following steps: 1. Take a natural number n. 2. Reverse its digits to get a new number. 3. Add the reversed number to the original number.
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A Lychrel number is a positive integer whose repeated reverse-and-add process never reaches a palindromic number in the chosen radix. Each step performs digit reversal and adds the reversed integer to the current value. For example, reaches a decimal palindrome in one step, so is not a base-ten Lychrel number.
Failure to reach a palindromic number within a fixed iteration limit establishes only a candidate. It does not prove that every later step also fails. A computation must therefore distinguish a bounded search result from the infinite claim in the definition.