# Definition:Palindromic Number

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## Definition

A **palindromic number (base $b$)** is a number which is a palindrome when expressed in number base $b$.

That is, it reads the same reversed as it does forwards.

When the base is not specified, it is commonplace to understand it as being $10$.

### Sequence

The sequence of **palindromic integers** in base 10 begins:

- $0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, \ldots$

## Also see

- Results about
**palindromic numbers**can be found**here**.

## Linguistic Note

The word **palindrome** derives from the Ancient Greek **παλίνδρομος** (**palíndromos**), meaning **running back again**.

This is formed from **πάλιν** (**pálin**), meaning **back**, **again**, and **back again**, and **δρόμος** (**drómos**), meaning **running**, **race**, and **racecourse**.

## Sources

- Weisstein, Eric W. "Palindromic Number." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/PalindromicNumber.html