Ars Combinatoria, vol.121, pp.187-200, 2015 (SCI-Expanded)
In this work, we first prove that every prime number p = 1 (mod 4) can be written of the form P2-4Q with two positive integers P and Q, and then we define the sequence Bn(P,Q) to be Bo = 2, Bi = P and Bn = PBn-i-QBn-2 for n > 2 and derive some algebraic identities on it. Also we formulate the limit of cross-ratio for four consecutive numbers Bn, B+i,Bn+2 and Bn+3-.