Distribution functions of ratio sequences. An expository paper

This expository paper presents known results on distribution functions g(x) of the sequence of blocks where x is an increasing sequence of positive integers. Also presents results of the set G(X ) of all distribution functions g(x). Specially: - continuity of g(x); - connectivity of G(Xn); - singleton of G(Xn); - one-step g(x); - uniform distribution of Xn, n = 1, 2, . . . ; - lower and upper bounds of g(x); - applications to bounds of - many examples, e.g., , where p is the nth prime, is uniformly distributed. The present results have been published by 25 papers of several authors between 2001-2013.