Pair correlation of fractional parts derived from rational valued sequences

We investigate the pair correlation of the sequence of fractional parts of αx_n, n∈N, where x_n is rational valued and α is a real number. As examples, we offer two classes of sequences x_n whose pair correlation behaves as that of random sequences for almost all real numbers α. First, sequences of the form x_n=a_n/b_n where a_n is lacunary and b_n satisfies a certain growth condition. Second, sequences of the form x_n=gⁿ/2^ω(n) for a positive integer g which is not a power of 2 and where ω(n) denotes the number of distinct prime factors of n.