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.