Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences

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Altassan A., Alan M.

MATHEMATICS, cilt.11, sa.2, ss.1-16, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/math11020455
  • Dergi Adı: MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1-16
  • Anahtar Kelimeler: k-Fibonacci numbers, repdigits, almost repdigits, linear forms in logarithms, MR imaging, tiny golden angles, k-generalized tiny golden angles
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the k-generalized Fibonacci sequence which are almost repdigits. In particular, we find all k-generalized Fibonacci numbers which are powers of 10 as a special case of almost repdigits. In the second part of the paper, by using the roots of the characteristic polynomial of the k-generalized Fibonacci sequence, we introduce k-generalized tiny golden angles and show the feasibility of this new type of angles in application to magnetic resonance imaging.