Cross-correlation between simultaneously generated sequences of pseudo-random uniform deviates

Systematic patterns are revealed when sequences of pseudo-random uniform deviates are generated from multiplicative congruential generators. If the initial seeds, x₀ and y₀, for two such sequences are related by y₀ = (n₁/n₂)x₀, where n₁ and n₂ are relatively prime, positive integers, then an approximate argument suggests that the asymptotic correlation coefficient between corresponding members of the two sequences is (n₁n₂)^–1. This unsettling phenomenon is discussed in the context of related, existing literature.