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Uzun, Yusuf
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Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology Physics

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Properties and Generalizations of Altered Jacobsthal Numbers Squared and their GCD Sequences Koken, Fikri; Ergun, Halime; Uzun, Yusuf
Science and Technology Indonesia Vol. 10 No. 1 (2025): January
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2025.10.1.273-282

Abstract

This paper investigates two types of altered Jacobsthal numbers, namely G(2)J(n) (a) and H(2)J(n) (a), which are obtained by adding or subtracting a specific value, denoted with {a}, from the square of the nth Jacobsthal numbers. These numbers exhibit a close relationship with the consecutive products of the Jacobsthal numbers. The study establishes consecutive sum-subtraction relations for the altered Jacobsthal numbers, and derives their Binet-like formulas. Furthermore, the greatest common divisor (Gcd) sequences of r-successive terms, represented by {G(2)J(n),r (a)} and {H(2)J(n),r (a)}, r ∈ {1, 2, 3, 4} are investigated. It is observed that these sequences display either a periodic or Jacobsthal structure.
Co-Authors Ergun, Halime Koken, Fikri