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

Kocapinar C., Ozkoq A., TEKCAN A.

Ars Combinatoria, vol.121, pp.187-200, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 121
  • Publication Date: 2015
  • Journal Name: Ars Combinatoria
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.187-200
  • Keywords: Binet's formula, Cross-ratio, Fibonacci, Lucas, Pell numbers
  • Bursa Uludag University Affiliated: Yes

Abstract

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-.