Let's call $S$ the infinite string that is made by concatenating the consecutive positive integers written down in base $10$. Thus, $$S = 12345678910111213141516171819202122232425\ldots$$
Any number in $S$ occurs multiple times. The first occurrence of $3$ is in the third position of the series, the second occurrence is in the seventeenth position, and so on.
How do I find the position of the hundredth occurrence of $3$? Is there a pattern?