  In these notes we address the study of the log-concave operator acting on
Lucas Sequences of first kind. We will find for which initial values a generic
Lucas sequence is log-concave, and using this we show when the same sequence is
infinite log-concave. The main result will help to find the log-concavity of
some well known recurrent sequences like Fibonacci and Mersenne. Some possible
generalization for a complete classification of the log-concave operator
applied to general linear recurrent sequences is proposed.
