The integer sequence B = Bn(P, Q) with parameters P and Q

Abstract

In this work, we first prove that every prime number p equivalent to 1 (mod 4) can be written of the form P-2-4Q with two positive integers P and Q, and then we define the sequence B-n(P, Q) to be B-0 = 2, B-1 = P and B-n = P Bn-1 - QB(n-2) for n >= 2 and derive some algebraic identities on it. Also we formulate the limit of cross ratio for four consecutive numbers B-n, Bn+1, Bn+2 and Bn+3.