Editing Palindrome (section)

=== Numbers ===
{{Main|Palindromic number}} {{Main|Periodic continued fraction}}
[[File:Immatriculation palyndromique.jpg|thumb|Palindromic license plate number]]

The digits of a palindromic number are the same read backwards as forwards, for example, 91019; [[decimal]] representation is usually assumed. In [[recreational mathematics]], palindromic numbers with special properties are sought. For example, 191 and 313 are [[palindromic prime]]s.

Whether [[Lychrel number]]s exist is an unsolved problem in mathematics about whether all numbers become palindromes when they are continuously reversed and added. For example, 56 is not a Lychrel number as 56 + 65 = 121, and 121 is a palindrome. The number 59 becomes a palindrome after three iterations: 59 + 95 = 154; 154 + 451 = 605; 605 + 506 = 1111, so 59 is not a Lychrel number either. Numbers such as 196 are thought to never become palindromes when this reversal process is carried out and are therefore suspected of being Lychrel numbers. If a number is not a Lychrel number, it is called a "delayed palindrome" (56 has a delay of 1 and 59 has a delay of 3). In January 2017 the number 1,999,291,987,030,606,810 was published in OEIS as [[oeis:A281509|A281509]], and described as "The Largest Known Most Delayed Palindrome", with a delay of 261. Several smaller 261-delay palindromes were published separately as [[oeis:A281508|A281508]].

Every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater.<ref>{{cite arXiv|last1=Cilleruelo|first1=Javier|last2=Luca|first2=Florian|last3=Baxter|first3=Lewis|date=19 February 2016|title=Every positive integer is a sum of three palindromes|eprint=1602.06208|class=math.NT}}</ref>