In this paper, an equation is provided for locating the first occurance of any 10^n number:
My question is if there is a generalized version of this equation that locates any number (eg, 314159), not just a 10^n number.
Seems like out of all the constants, the Champernowne constant would have such a function since its digits are engineered already.
Also, note: I am not asking for a function that returns the nth digit, rather the digits' nth-ness.
Edit: here is some visual to show what is going on. Horizontal axis denotes number to find, and vertical axis denotes that number's position.