> The answer is yes, p_i/p_j is dense in R+. I think that this is > a special case of the following lemma with f(x) = x log x:
Another way of looking at it is to note that p(x) ~ x*ln(x), and so lim p([rx])/p(x) = r. If I'm not mistaken, the more general result you mention can be found in Kuipers et. al. _Uniform Distribution of Sequences_.