A self-descriptive number $n$ in base $b$ is an integer such that each base $b$ digit $$d_x = \sum_{d_i = x} 1$$ where each $d_i$ is a digit of $n$ , $i$ is a very simple, standard iterator operating in the range $-1 < i < b$ , and $x$ is a position of a digit; thus $n$ ``describes'' itself.

For example, the integer 6210001000 written in base 10. It has six instances of the digit 0, two instances of the digit 1, a single instance of the digit 2, a single instance of the digit 6 and no instances of any other base 10 digits.

Base 4 might be the only base with two self-descriptive numbers, $1210_4$ and $2020_4$ . From base 7 onwards, every base $b$ has at least one self-descriptive number of the form $(b - 4)^{b - 1} + 2b^{b - 2} + b^{b - 3} + b^4$ . It has been proven that 6210001000 is the only self-descriptive number in base 10, but it's not known if any higher bases have any self-descriptive numbers of any other form.

Sequence A108551 of the OEIS lists self-descriptive numbers from quartal to hexadecimal.