# Repdigit

In recreational mathematics, a repdigit or sometimes monodigit[1] is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word repdigit is a portmanteau, formed from repeated digit.

Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. One of the most famous repdigits is 666, referred to in Christian Eschatology as the number of the beast. Other well-known repdigits include the repunit primes and in particular the Mersenne primes (when represented in binary).

Repdigits are the representation in base $B$ of the number $x\frac{B^y -1}{B-1}$ where $0 is the repeated digit and $y$ is the number of repetitions. For example, the repdigit 77 in base 10 is $7\times\frac{10^2-1}{10-1}$.

## References

1. ^ Beiler, Albert (1966). Recreations in the Theory of Numbers: The Queen of Mathematics Entertains (2 ed.). New York: Dover Publications. p. 83. ISBN 978-0-486-21096-4.