1
Bitlis Eren University, Faculty of Science and Arts, Department of Mathematics, Bitlis, T¨urkiye
(hgokbas@beu.edu.tr)
2
Bitlis Eren University, Faculty of Science and Arts, Department of Mathematics, Bitlis, T¨urkiye
(s.topal@beu.edu.tr)
3
Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA
(smarand@unm.edu)
Abstract :
In this paper, Neutrosophic definitions and properties of some special number sequences which are frequently found in the science literature, called Neutrosophic Number Sequences (NNSq) via Horadam sequence are studied for the first time. Especially for Neutrosophic Fibonacci (NFNq) and Neutrosophic Lucas (NLNq) number sequences, fundamental properties and identities such as Ruggles, Honsberger, Cassini, Catalan, d’Ocagne, and Tagiuri are given. In addition, Neutrosophic definitions of the sequences of Pell (NPNq), Pell-Lucas (NPLNq), Jacobsthal (NJNq), Jacobsthal-Lucas (NJLNq), Mersenne (NMNq), Mersenne-Lucas (NMLNq), Balancing (NBNq), and Lucas-Balancing (NLBNq) numbers are introduced. Besides defining these numbers and their sequences, since fuzzy and intuitionistic fuzzy sets are restrictions of neutrosophic sets, sequences of numbers within these sets are naturally and indirectly revealed.
Keywords :
Neutrosophic number sequence; Neutrosophic fibonacci number sequence; Neutrosophic lucas
number sequence; Neutrosophic pell number sequence; Neutrosophic Jacobsthal number sequence; Neutrosophic
jacobsthal-lucas number sequence; Neutrosophic mersenne number sequence; Neutrosophic mersennelucas
number sequence; Neutrosophic balancing number sequence; Neutrosophic lucas-balancing number sequence;
Horadam Form
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| Style | # |
|---|---|
| MLA | Hasan Gökbas , Selçuk Topal, Florentin Smarandache. "Neutrosophic Number Sequences: An introductory Study." International Journal of Neutrosophic Science, Vol. 20, No. 1, 2023 ,PP. 27-48 (Doi : https://doi.org/10.54216/IJNS.200103) |
| APA | Hasan Gökbas , Selçuk Topal, Florentin Smarandache. (2023). Neutrosophic Number Sequences: An introductory Study. Journal of International Journal of Neutrosophic Science, 20 ( 1 ), 27-48 (Doi : https://doi.org/10.54216/IJNS.200103) |
| Chicago | Hasan Gökbas , Selçuk Topal, Florentin Smarandache. "Neutrosophic Number Sequences: An introductory Study." Journal of International Journal of Neutrosophic Science, 20 no. 1 (2023): 27-48 (Doi : https://doi.org/10.54216/IJNS.200103) |
| Harvard | Hasan Gökbas , Selçuk Topal, Florentin Smarandache. (2023). Neutrosophic Number Sequences: An introductory Study. Journal of International Journal of Neutrosophic Science, 20 ( 1 ), 27-48 (Doi : https://doi.org/10.54216/IJNS.200103) |
| Vancouver | Hasan Gökbas , Selçuk Topal, Florentin Smarandache. Neutrosophic Number Sequences: An introductory Study. Journal of International Journal of Neutrosophic Science, (2023); 20 ( 1 ): 27-48 (Doi : https://doi.org/10.54216/IJNS.200103) |
| IEEE | Hasan Gökbas, Selçuk Topal, Florentin Smarandache, Neutrosophic Number Sequences: An introductory Study, Journal of International Journal of Neutrosophic Science, Vol. 20 , No. 1 , (2023) : 27-48 (Doi : https://doi.org/10.54216/IJNS.200103) |