Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 2, Pages 331–338
DOI: 10.7546/nntdm.2022.28.2.331-338
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Authors and affiliations
Krassimir T. Atanassov
Department of Bioinformatics and Mathematical Modelling,
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
Acad. G. Bonchev Str. Bl. 105, Sofia-1113, Bulgaria
Abstract
A new scheme of 2-Fibonacci sequences is introduced and the explicit formulas for its n-th members are given. For difference of all previous sequences from Fibonacci type, the present 2-Fibonacci sequences are obtained by a new way. It is proved that the new sequences have bases with 48 elements about function 𝜑 and modulo 9.
Keywords
- Fibonacci sequence
- 2-Fibonacci sequence
2020 Mathematics Subject Classification
- 11B39
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Manuscript history
- Received: 12 March 2022
- Revised: 11 May 2022
- Accepted: 11 May 2022
- Online First: 12 May 2022
Related papers
- Atanassov, K. (2010). Combined 2-Fibonacci sequences. Notes on Number Theory and Discrete Mathematics, 16(2), 24–28.
- Atanassov, K. (2010). Combined 2-Fibonacci sequences. Part 2. Notes on Number Theory and Discrete Mathematics, 16(4), 18–24.
- Atanassov, K. (2015). A digital arithmetical function and some of its applications.
Proceedings of the Jangjeon Mathematical Society, 18(4), 511–528. - Atanassov, K., & Shannon, A. (2016). Combined 3-Fibonacci sequences from a new type. Notes on Number Theory and Discrete Mathematics, 22(3), 5–8.
- Atanassov, K. (2018). On two new combined 3-Fibonacci sequences. Notes on Number Theory and Discrete Mathematics, 24(2), 90–93.
- Atanassov, K. (2018). On two new combined 3-Fibonacci sequences. Part 2. Notes on Number Theory and Discrete Mathematics, 24(3), 111–114.
- Atanassov, K. (2022). On two new combined 3-Fibonacci sequences, Part 3. Notes on Number Theory and Discrete Mathematics, 28(1), 143–146.
- Ma, T., Vernon. R., & Arora, G. (2024). Generalization of the 2-Fibonacci sequences and their Binet formula. Notes on Number Theory and Discrete Mathematics, 30(1), 67-80.
Cite this paper
Atanassov, K. T. (2022). Two 2-Fibonacci sequences generated by a mixed scheme. Part 1. Notes on Number Theory and Discrete Mathematics, 28(2), 331-338, DOI: 10.7546/nntdm.2022.28.2.331-338.