  Let x be a quadratic irrational and let P be the set of prime numbers. We
show the existence of an infinite subset S of P such that the statistics of the
period of the continued fraction expansions along the sequence {px: p\in S}
approach the normal statistics given by the Gauss-Kuzmin measure. Under the
generalized Riemann hypothesis, we prove that there exist full density subsets
S of P and T of N satisfying the same assertion. We give a rate of convergence
in all cases.
