nonLychrel

nonLychrel is a term used in recreational mathematics to describe a number that is not a Lychrel number. A Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the reversed number to the original number. If a number never forms a palindrome, it is considered a Lychrel number. Conversely, a nonLychrel number is one that eventually results in a palindrome after a finite number of these reversals and additions.

The process for determining if a number is nonLychrel involves starting with the number, reversing its digits, and adding the reversed number to the original. If the sum is a palindrome, the original number is nonLychrel. If the sum is not a palindrome, the process is repeated with the sum. This process continues until a palindrome is found.

For example, the number 56 is a nonLychrel number. When you reverse 56 to get 65 and add them, you get 56 + 65 = 121. Since 121 is a palindrome, 56 is confirmed to be a nonLychrel number. Many numbers are quickly identified as nonLychrel numbers because they produce palindromes within a few steps.

The existence of true Lychrel numbers (numbers that are proven to never form a palindrome) has not been definitively established. All numbers tested up to very large magnitudes have eventually produced a palindrome. However, it is conjectured that true Lychrel numbers exist. Therefore, any number that has not been proven to be a Lychrel number is considered, by definition, a nonLychrel number.

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