# Problem 305: Reflexive Position
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... It's easy to see
that any number will show up an infinite number of times in S. Let's
call f(n) the starting position of the nth occurrence of n in S. For
example, f(1)=1, f(5)=81, f(12)=271 and f(7780)=111111365. Find ∑f(3k)
for 1≤k≤13.