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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" or even "Malayalam") whose spelling is unchanged when its letters are reversed. The first 30 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, 202, … . 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, … . *The palindromic square numbers are 0, 1, 4, 9, 121, 484, 676, 10201, 12321, … . 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 ''n''th number is a 1, followed by ''n'' zeros, followed by a 1) consists of palindromic numbers only. ==Formal definition== Although palindromic numbers are most often considered in the decimal system, the concept of palindromicity can be applied to the natural numbers in any numeral system. Consider a number ''n'' > 0 in base ''b'' ≥ 2, where it is written in standard notation with ''k''+1 digits ''a''''i'' as: : with, as usual, 0 ≤ ''a''''i'' < ''b'' for all ''i'' and ''a''''k'' ≠ 0. Then ''n'' is palindromic if and only if ''a''''i'' = ''a''''k''−''i'' for all ''i''. Zero is written 0 in any base and is also palindromic by definition. 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「Palindromic number」の詳細全文を読む スポンサード リンク
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