> 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_.
-Chris
If a sequence {a_n} is asymptotic to f(n), where f is a continuous
function satisfying
f'(x)/f(x) = o(1)
limsup f(x) = infinity
f'(x) > 0.
then a_i/a_j is dense in R+.
Stanford Sabbatical Problem Solving Group = {Ted Alper, Ilan Vardi}