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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 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 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lychrel number」の詳細全文を読む スポンサード リンク
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