%0 Journal Article
%T On weighted distribution functions of sequences
%A Rita Giuliano Antonini
%A Oto Strauch
%J Uniform Distribution Theory
%D 2008
%I Mathematical Institute of the Slovak Academy of Sciences
%X In this paper we prove that the set of logarithmically weighted distribution. In this paper we prove that the set of logarithmically weighted distribution functions of the sequence of iterated logarithm $\log^{(i)}n \bmod 1$, $n = n_i,n_i+1, \dots$ is the same as the set of classical distribution functions of the sequence $\log^{(i-1)}n \bmod 1$ for every $i=2,3, \dots$. Also we prove that $\log(n \log n)$ $\bmod 1 $is logarithmically uniformly distributed. This implies that the sequence $p_n/n mod 1$, where $p_n$ denotes the $n$th prime, is also logarithmically uniformly distributed.
%K Distribution function
%K weights
%K Helly theorems
%U http://www.boku.ac.at/MATH/udt/vol03/no1/GiuSt08-1.pdf