Repdigit

In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system.

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.

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

The word repdigit is a portmanteau, formed from repeated digit.

See also

• Feynman point
• Repunit

References

• Weisstein, Eric W. "Repdigit". MathWorld.