repdigit

Given base $b$, a number of the form $d(\frac{b^n-1}{b-1})$ for $n>0$ and is written using using the digit $d$ only, $n$ times in that base and is therefore a repdigit. The term, short for ”repeated digit,” is credited to Beiler’s book Recreations in the theory of numbers, in chapter 11.

When $d=1$, the resulting repdigit is called a repunit. Only repunits can also be prime (and then they are rare). No other repdigit can be prime since it is obvious that it is a multiple of a repunit.

In a trivial way, all repdigits are palindromic numbers.

Title	repdigit
Canonical name	Repdigit
Date of creation	2013-03-22 16:20:14
Last modified on	2013-03-22 16:20:14
Owner	CompositeFan (12809)
Last modified by	CompositeFan (12809)
Numerical id	5
Author	CompositeFan (12809)
Entry type	Definition
Classification	msc 11A63