Lychrel Number - Reverse and Add Process

Reverse and Add Process

The reverse and add process produces the sum of a number and the number formed by reversing the order of its digits. e.g. 56 + 65 = 121, 125 + 521 = 646.

Some numbers become palindromes quickly after repeated reversal and addition, and are therefore not Lychrel numbers. All 1 digit and 2 digit numbers eventually become palindromes after repeated reversal and addition. About 80% of all numbers under 10,000 resolve into a palindrome in 4 or fewer steps. About 90% solve in 7 steps or less. Here are a few examples of non-Lychrel numbers:

• 56 becomes palindromic after one iteration: 56+65 = 121.
• 57 becomes palindromic after two iterations: 57+75 = 132, 132+231 = 363.
• 59 becomes a palindrome after 3 iterations: 59+95 = 154, 154+451 = 605, 605+506 = 1111
• 89 takes an unusually large 24 iterations (the most of any number under 10,000 that is known to resolve into a palindrome) to reach the palindrome 8813200023188.
• 10,911 reaches the palindrome 4668731596684224866951378664 after 55 steps.
• 1,186,060,307,891,929,990 takes 261 iterations to reach the 119 digit palindrome 44562665878976437622437848976653870388884783662598425855963436955852489526638748888307835667984873422673467987856626544, which is the currently known world record for the Most Delayed Palindromic Number. It was solved by Jason Doucette's algorithm and program (using Benjamin Despres' reversal-addition code) on November 30, 2005.

The first known number starting from 0 that does not apparently form a palindrome is a three digit number, 196. It is the smallest Lychrel number candidate.