Lychrel

Lychrel numbers are a class of numbers that do not form a palindrome through the iterative process of repeatedly reversing its digits and adding the result to the original number. This process is known as the "196-algorithm," named after the number 196, which was the first number proven to be a Lychrel number. The term "Lychrel" was coined by mathematician John Conway.

The 196-algorithm is defined as follows: take a number, reverse its digits, and add the reversed number to the original. If the result is not a palindrome, repeat the process with the new number. If a palindrome is eventually formed, the original number is not a Lychrel number. However, if no palindrome is formed after a certain number of iterations (typically 50), the number is considered a Lychrel number.

Lychrel numbers are rare. It is conjectured that only a small percentage of numbers are Lychrel numbers, but this has not been proven. The largest known non-Lychrel number is 10^1022, and the largest known Lychrel number is 249996, which was found in 2019.

The properties of Lychrel numbers are still an active area of research in number theory. The study of Lychrel numbers has led to the discovery of other interesting mathematical properties and has sparked curiosity in the mathematical community.