Let's call $S$ the (infinite) string that is made by concatenating the consecutive positive integers (starting from 1) written down in base 10. Thus, $S = 1234567891011121314151617181920212223242\ldots$
Any number in $S$ occurs multiple times. The first occurence of 3 is in position 3 of the series, 2nd occurence is in position 17.
How do I find the position of 3 in 100th occurence? Is there a pattern?