Neutrosophic Number Sequences: An introductory Study

Hasan G¨okbas¸1, Selc¸uk Topal2,∗, Florentin Smarandache 3

1 , 2Bitlis Eren University, Faculty of Science and Arts, Department of Mathematics, Bitlis, T¨urkiye

3Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA

Emails: hgokbas@beu.edu.tr1; s.topal@beu.edu.tr ( selcuk.topal@yandex.com)2; smarand@unm.edu3

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