Article Dans Une Revue Asian Research Journal of Mathematics Année : 2025

A Study on Altered Jacobsthal Lucas Numbers Squared: Structural Properties and Applications

Résumé

We examine two variations of the Jacobsthal Lucas numbers, denoted as \(G^{(2)}_{j(n)}\)(a) and \(H^{(2)}_{j(n)}\)(a) which are derived through the addition or subtraction of a specific value {a} from the square of the nth Jacobsthal Lucas numbers due to their relevance to the products of Jacobsthal numbers. Consequently we derive both the consecutive sum-subtraction relationships and Binet-like expressions for these altered sequences, while also investigating 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)} for r ∈ {1, 2, 3, 4}, which are informed by the periodic properties of the Gcd ofconsecutive Jacobsthal numbers.

Dates et versions

hal-05053206 , version 1 (01-05-2025)

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Citer

Fikri Koken. A Study on Altered Jacobsthal Lucas Numbers Squared: Structural Properties and Applications. Asian Research Journal of Mathematics, 2025, 21 (5), pp.115-131. ⟨10.9734/arjom/2025/v21i5928⟩. ⟨hal-05053206⟩
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