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 resulting numbers. This process is sometimes called the 196-algorithm, after the most famous number associated with the process. In base ten, no Lychrel numbers have been yet proved to exist, but many, including 196, are suspected on heuristic and statistical grounds. The name "Lychrel" was coined by Wade Van Landingham as a rough anagram of Cheryl, his girlfriend's first name.

The reverse-and-add process produces the sum of a number and the number formed by reversing the order of its digits. For example, 56 + 65 = 121. As another example, 125 + 521 = 646.

Some numbers become palindromes quickly after repeated reversal and addition, and are therefore not Lychrel numbers. All one-digit and two-digit numbers eventually become palindromes after repeated reversal and addition.

About 80% of all numbers under 10,000 resolve into a palindrome in four or fewer steps. About 90% resolve in seven steps or fewer. Here are a few examples of non-Lychrel numbers:

The smallest known number that is not known to form a palindrome is 196. It is the smallest Lychrel number candidate.

The number resulting from the reversal of the digits of a Lychrel number is also a Lychrel number.

In other bases (these bases are power of 2, like binary and hexadecimal), certain numbers can be proven to never form a palindrome after repeated reversal and addition, but no such proof has been found for 196 and other base 10 numbers.

It is conjectured that 196 and other numbers that have not yet yielded a palindrome are Lychrel numbers, but no number in base ten has yet been proven to be Lychrel. Numbers which have not been demonstrated to be non-Lychrel are informally called "candidate Lychrel" numbers. The first few candidate Lychrel numbers (sequence in the OEIS) are:

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