Interesting sequence mod p

Number Theory Level pending

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 \[ \lim_{n \to \infty} \frac{a_{n}}{n} - \frac{3}{4}\]

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