Branch Mathematics and Statistics Faculty and Staff Publications

Document Type

Article

Publication Date

2022

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.

Publisher

International Journal of Neutrosophic Science (IJNS)

Publication Title

Neutrosophic Number Sequences: An introductory Study

Language (ISO)

English

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 Mersenne-Lucas number sequence; Neutrosophic balancing number sequence; Neutrosophic Lucas-balancing number sequence; Horadam Form

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