 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 heuristichttp://mathoverflow.net/questions/117104/status-of-the-196-conjecture/117277#117277 and statistical grounds. the name "lychrel" was coined by wade vanlandingham as a rough anagram of cheryl, his girlfriend's first name. == 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. 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: *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 8,813,200,023,188. *10,911 reaches the palindrome 4668731596684224866951378664 (28 digits) after 55 steps. *1,186,060,307,891,929,990 takes 261 iterations to reach the 119-digit palindrome 44562665878976437622437848976653870388884783662598425855963436955852489526638748888307835667984873422673467987856626544, which is the current 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 smallest known number that apparently does not form a palindrome is a three-digit number, 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. == proof not found == 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
Number_theory Unsolved_problems_in_mathematics