aspg-21-1428-1791468697 20261008141137 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 20 1 Hasan Gökbas Bitlis Eren University, Faculty of Science and Arts, Department of Mathematics, Bitlis, T¨urkiye Selçuk Topal Bitlis Eren University, Faculty of Science and Arts, Department of Mathematics, Bitlis, T¨urkiye Florentin Smarandache Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA 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. 2023 27 48 1428 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.200103 https://www.americaspg.com/journal/21/article/1428 https://www.americaspg.com/storage/31672827862.pdf