Interesting sequence mod p

Let $x_{n}$ be a sequence of positive integers with $x_{1}=1$ and for any prime number $p$ the set $\{x_{1},x_{2},...,x_{p}\}$ is a complete residue system $\pmod{p}$ . Then what is the value of the limit $\lim_{n \to \infty} \frac{a_{n}}{n} - \frac{3}{4}$