CONDITIONAL (STRONG) DIVISIBILITY SEQUENCES

ŞAHİN M., TAN E.

FIBONACCI QUARTERLY, cilt.56, sa.1, ss.18-31, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 56 Sayı: 1
  • Basım Tarihi: 2018
  • Dergi Adı: FIBONACCI QUARTERLY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.18-31
  • Ankara Üniversitesi Adresli: Evet

Özet

A conditional recurrence sequence {q(n)} is one in which the recurrence satisfied by q(n) depends on the residue of n modulo some integer r >= 2. If a conditional sequence {q(n)} is a (strong) divisibility sequence then we define it as a conditional (strong) divisibility sequence. In this paper, we find some families of the conditional (strong) divisibility sequences for r = 2. These sequences are a generalization of the best known (strong) divisibility sequences in the literature, such as the Fibonacci sequence, the Lucas sequence, the Lehmer sequence, etc. Also, they contain some new fourth-order linear divisibility sequences which are different from the ones in the literature. An open problem is to determine the conditional (strong) divisibility sequences for r > 2.