# Lucas sequences

Lucas sequences are generalizations of the Fibonacci
sequence and were first investigated by Edouard Lucas.
One kind can be defined as follows: *L*(0) = 0, *L*(1) = 1, *L*(*n* + 2)
= *PL*(*n *+ 1) + *QL*(*n*), where the normal Fibonacci
sequence is the special case of *P* = *Q* = 1. Another kind of
Lucas sequence begins with *L*(0) = 2, *L*(1) = *P*. Such
sequences are used in number theory and in testing for prime numbers.