I'll take a half-hearted empirical stab at this myself. The smallest base-ten number that contains the numbers from 1 to n as substrings (A035239) appears to be of length n. The period of a primitive-root-10 prime (A001913) p is p-1, so it can contain all d-digit numbers only if p-1 >= 10^d-1. Which leaves why p should happen to be the *first* member of A001913 > 10^d (and not some subsequent one). I wrote:
David Wilson:
I realized that this sequence would be a(n) = smallest prime >= 10^n with primitive root 10.
The primitive-root-10 (A001913) criterion assures us a large decimal expansion period from which to cull our n-digit collection. That is also shared by primitive-root-10 primes < 10^n. How do you know one of these doesn't eventually luck into a 9*10^(n-1) distinct n-digit count?