The integer sequence B = Bn(P,Q) with parameters P and Q
Ars Combinatoria, cilt.121, ss.187-200, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 121
- Basım Tarihi: 2015
- Dergi Adı: Ars Combinatoria
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.187-200
- Anahtar Kelimeler: Binet's formula, Cross-ratio, Fibonacci, Lucas, Pell numbers
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
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-.