%0 Journal Article
%T On the $1/3$ density of odd ranked primes in Lucas sequences
%A Christian Ballot
%J Uniform Distribution Theory
%D 2008
%I Mathematical Institute of the Slovak Academy of Sciences
%X It seems that companion Lucas sequences often have a two-third density of prime divisors. Is it indeed the case? And if so, why? In this paper we present heuristics that predict this $2/3$ proportion before actually proving that $2/3$ is the correct prime density for almost all companion Lucas sequences.
%K Prime density
%K Lucas sequence
%K Legendre symbol
%K number field.
%U http://www.boku.ac.at/MATH/udt/vol03/no2/Ballot08-2.pdf