Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences
MATHEMATICS, cilt.11, sa.2, ss.1-16, 2023 (SCI-Expanded, Scopus)
- 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.