What do you call a number which is the same written backwards? Example 16061.


Palindrome /…/ noun a word, phrase, or sequence that reads the same backward as forward

This excerpt is from the Oxford Dictionary of English, third edition, which was edited by Angus Stevenson.

In the definition, a sequence refers to number chains. If you didn't want to be completely on the nose about it, you could work in the phrase mirror image to describe what you need as well.

  • Indeed, palindrome also describes musical sequences that are the same backwards. kottke.org/17/02/bachs-crab-canon-is-a-musical-palindrome – rajah9 Mar 27 '17 at 15:51
  • Although you have made it obvious that this is a quote from somewhere, please also provide the source in plain text (and a link if possible), following Stack Exchange policy. – Andrew Leach Mar 27 '17 at 16:35
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    I would generally use the adjective form myself. Palindrome reads as referring a word to my mind, so palindromic number would be the equivalent number. – Bobson Mar 27 '17 at 18:41
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    @Bobson One could as easily refer to a numeric palindrome. But if the context is clear ("Is the result of this calculation a palindrome?") then no adjective is needed to differentiate numeric palindromes from the ordinary alphabetic sort. – Monty Harder Mar 27 '17 at 20:01
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    If you used the phrase "mirror image", I'd expect some sort of reflective symmetry: for example, "08080" is both a palindrome and a mirror image, while "12421" is a palindrome but not a mirror image. – Mark Mar 27 '17 at 23:57

The correct mathematical term is a palindromic number (or a numerical palindrome).

To quote Wikipedia:

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.

And for a more mathematical definition from Wolfram:

A palindromic number is a number (in some base b) that is the same when written forwards or backwards, i.e., of the form a_1a_2...a_2a_1. The first few palindromic numbers are therefore are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, ... (OEIS A002113).

These in turn are used to form the derived terms palindromic prime and strictly non-palindromic number.

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