Consider the following sequence: $$1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 2, 0, 2, 1, 2, 2, 2, 3, \ldots$$ which is formed by extracting the digits of the natural numbers. Is there any formula for the general term of this sequence?
All I can think of is an algorithm to obtain its terms:
"Set $n = 1$. While $n$ is not too big {extract digits from $n$ and insert them into the sequence, then set $n = n + 1$}"