Results 1 to 10 of about 167 (139)
Elliptic Solutions of Dynamical Lucas Sequences [PDF]
Entropy, 2021 We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system
Michael J. Schlosser, Meesue Yoo
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Relations between Generalized Bi-Periodic Fibonacci and Lucas Sequences [PDF]
Mathematics, 2020 In this paper we consider a generalized bi-periodic Fibonacci {fn} and a generalized bi-periodic Lucas sequence {qn} which are respectively defined by f0=0, f1=1, fn=afn−1+cfn−2 (n is even) or fn=bfn−1+cfn−2 (n is odd), and q0=2d, q1=ad, qn=bqn−1+cqn−2 ...
Younseok Choo
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A Context-Free Grammar Associated with Fibonacci and Lucas Sequences
Journal of Mathematics, 2023 We introduce a context-free grammar G=s⟶s+d,d⟶s to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula.
Harold Ruilong Yang
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Equations with Solution in Terms of Fibonacci and Lucas Sequences [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 The main results characterize the equations (2.1) and (2.10) whose solutions are linear combinations with rational coefficients of at most two terms of classical Fibonacci and Lucas sequences.
Andreescu Titu, Andrica Dorin
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On Fibonacci and Lucas sequences modulo a prime and primality testing
Arab Journal of Mathematical Sciences, 2018 We prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p∣Fp−p5. We then discuss these results in the context of primality testing.
Dorin Andrica +2 more
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Some Notes on Odd or Even Indexed Fibonacci And Lucas Sequences
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019 The uniqueness of the sum of the elements of finite subsets of the odd oreven indexed Fibonacci and Lucas sequences are proved. Moreover, it is shownthat the odd or even indexed Fibonacci and Lucas sequences are superincreasingsequences.
Alparslan Kargın +2 more
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Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu +1 more
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On the k-Fibonacci and k-Lucas spinors [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we introduce a new family of sequences called the k-Fibonacci and k-Lucas spinors. Starting with the Binet formulas we present their basic properties, such as Cassini’s identity, Catalan’s identity, d’Ocagne's identity, Vajda's identity ...
Munesh Kumari +2 more
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Solutions of equations x2−(p2q2±3p)y2=±kt
Examples and Counterexamples, 2022 In the present paper, we have solved the equation x2−(p2q2±3p)y2=kt,x2−(p2q2±5p)y2=ktand expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences.
Roji Bala, Vinod Mishra
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Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences [PDF]
Turkish Journal of Analysis and Number Theory, 2016 The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula Fn=Fn-1+Fn-2, , and F0=0, F1=1, where Fn is a nth number of sequence.
Yogesh Kumar Gupta +2 more
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