Recently I heard about autobiographical numbers. They are kind of self-descriptive numbers, where the $i$-th digit at is the number of occurrences of the digit $i$ in the number. For example, consider $1210$. Its first digit $1$ is the number of $0$s in the number; the next digit $2$ is the number of $1$s in the number, and so on.
My question is: Is it be possible for any formula to yield the $n$-th autobiographical number (the sequence is starting from $1210$ and goes on)?