Repdigits

A repdigit is a natural number composed of repeating instances of the same digit. For example, 11, 222, 3333, and 777777 are repdigits. The term repdigit is a portmanteau of "repeat" and "digit".

Repdigits can be represented mathematically. A repdigit consisting of the digit 'd' repeated 'n' times can be written as d * (10^n - 1) / 9, where 'd' is a digit from 1 to 9, and 'n' is a positive integer representing the number of times the digit repeats. For instance, the repdigit 444 is equal to 4 * (10^3 - 1) / 9 = 4 * 999 / 9 = 4 * 111 = 444.

Repdigits have interesting properties in number theory. For example, any repdigit with an even number of digits is divisible by 11. A repdigit with a number of digits that is a multiple of 3 is divisible by 3 and 37.

The concept of repdigits is also explored in recreational mathematics. Identifying repdigits or exploring their divisibility rules can be a common pastime for number enthusiasts. In certain contexts, such as sequences or patterns, repdigits appear naturally.