Some properties of a special set of recurring sequences
Hugh C. Williams · Pacific Journal of Mathematics · 1978
Several number theoretic and identity properties of three special second order recurring sequences are established. These are used to develop a necessary and sufficient condition for any integer of the form 2n3mA — 1 (A n — 1 when A < 4 3 U — 1. Of special concern to Riesel was the determination of the primality of 3A2 % — 1; in this paper we present a simple necessary and sufficient condition for 2n3mA — 1 to be prime when A < 2n+1Zm — 1. In order to obtain this result we must first develop some properties of a special set of second order linear recurring sequences. Let a, b be two integers and put a = a + bp, β — a + bp2, where p2 + p + 1 = 0. We define for any integer n Rn — p — p