Given base b, a number of the form d(bn-1b-1) for n>0 and 0<d<b 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 repunitMathworldPlanetmath. 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 multipleMathworldPlanetmath of a repunit.

In a trivial way, all repdigits are palindromic numbersMathworldPlanetmath.

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