repdigit

Given base $b$, a number of the form $d({{b^{n}-1}\over{b-1}})$ for $n>0$ and $0 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 Repdigit 2013-03-22 16:20:14 2013-03-22 16:20:14 CompositeFan (12809) CompositeFan (12809) 5 CompositeFan (12809) Definition msc 11A63