A palindromic number or numeral palindrome is a number that remains the same when its digits are reversed. Like 16461, for example, it is "symmetrical". The term palindromic is derived from palindrome, which refers to a word (such as rotor or racecar) whose spelling is unchanged when its letters are reversed. The first palindromic numbers (in decimal) are:
- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, … (sequence A002113 in OEIS).
Palindromic numbers receive most attention in the realm of recreational mathematics. A typical problem asks for numbers that possess a certain property and are palindromic. For instance:
- The palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, … (sequence A002385 in OEIS).
- The palindromic square numbers are 0, 1, 4, 9, 121, 484, 676, 10201, 12321, … (sequence A002779 in OEIS).
Buckminster Fuller referred to palindromic numbers as Scheherazade numbers in his book Synergetics, because Scheherazade was the name of the story-telling wife in the 1001 Nights.
It is fairly straightforward to appreciate that in any base there are infinitely many palindromic numbers, since in any base the infinite sequence of numbers written (in that base) as 101, 1001, 10001, etc. (in which the nth number is a 1, followed by n zeros, followed by a 1) consists of palindromic numbers only.
Read more about Palindromic Number: Formal Definition, Decimal Palindromic Numbers, Perfect Powers, Other Bases, Lychrel Process, Sum of The Reciprocals
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