Call the first digit of a number digit 0. The digit after that digit 1, and so on and so forth.
In base 10, the number 6210001000 describes itself, because digit 0 is 6 and it has 6 0s. Digit 1 is 2 and it has 2 1s. Digit 2 is 1 and there is only 1 2. There are none of the other numerals.
So it occurs to me that in duodecimal, you can do 821000001000, which is 6073061476032 in decimal. In base 40, you could do Z21000... something like that, you get the idea. You could keep going, the only problem being not having enough symbols.
According to a graphic I saw on Facebook, 6210001000 is the only such number in base 10. I'm wondering: might there be some base in which a number describes itself like this but its first digit isn't 4 less than the base, followed by 21 and a bunch of 0s with a 1 close to the end?