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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, $56+65=121$ reaches a decimal palindrome in one step, so $56$ 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.