Results 11 to 20 of about 183 (115)
The GCD Sequences of the Altered Lucas Sequences [PDF]
Annales Mathematicae Silesianae, 2020 In this study, we give two sequences {L+n}n≥1 and {L−n}n≥1 derived by altering the Lucas numbers with {±1, ±3}, terms of which are called as altered Lucas numbers.
Koken Fikri
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Mathematica Bohemica, 2021 Summary: Let \((G_{n})_{n\geq 1}\) be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are \(\{U_n\}\) and \(\{V_n\}\), respectively. We show that the Diophantine equation \(G_n=B\cdot(g^{lm}-1)/(g^{l}-1)\) has only finitely many solutions in \(n,m\in\mathbb{Z}^+\), where \(g\geq 2 ...
Hayder Raheem Hashim, Szabolcs Tengely
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Journal of the Indonesian Mathematical Society, 2023 Horadam introduced a generalized sequence of numbers, describing its key features and the special sub-sequences obtained from specific choices of initial parameters. This sequence and its sub-sequences are known as the Horadam, generalized Fibonacci, and generalized Lucas numbers, respectively.
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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 is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences
Schlosser, Michael J., Yoo, Meesue
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ON PERFECT POWERS IN LUCAS SEQUENCES [PDF]
International Journal of Number Theory, 2005 Let (un)n≥0be the binary recurrence sequence of integers given by u0= 0, u1= 1 and un+2= 2(un+1+ un). We show that the only positive perfect powers in this sequence are u1= 1 and u4= 16. We further discuss the problem of determining perfect powers in Lucas sequences in general.
Bugeaud, Yann +3 more
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On some new results for the generalised Lucas sequences
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica Dorin +2 more
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On r-Jacobsthal and r-Jacobsthal-Lucas Numbers
Annales Mathematicae Silesianae, 2023 Recently, Bród introduced a new Jacobsthal-type sequence which is called r-Jacobsthal sequence in current study. After defining the appropriate r-Jacobsthal–Lucas sequence for the r-Jacobsthal sequence, we obtain some properties of these two sequences ...
Bilgici Göksal, Bród Dorota
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Repdigits as difference of two Fibonacci or Lucas numbers
Математичні Студії, 2021 In the present study we investigate all repdigits which are expressed as a difference of two Fibonacci or Lucas numbers. We show that if $F_{n}-F_{m}$ is a repdigit, where $F_{n}$ denotes the $n$-th Fibonacci number, then $(n,m)\in \{(7,3),(9,1),(9,2 ...
P. Ray, K. Bhoi
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Additional Fibonacci-Bernoulli relations
Researches in Mathematics, 2022 We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli numbers and polynomials. The derivations of our results are based on functional equations for the respective generating functions, which in our case are combinations ...
K. Adegoke, R. Frontczak, T.P. Goy
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Oscillatory Nonautonomous Lucas Sequences [PDF]
International Journal of Differential Equations, 2009 The oscillatory behavior of the solutions of the second‐order linear nonautonomous equation x(n + 1) = a(n)x(n) − b(n)x(n − 1), n ∈ ℕ0, where a, b : ℕ0 → ℝ, is studied. Under the assumption that the sequence b(n) dominates somehow a(n), the amplitude of the oscillations and the asymptotic behavior of its solutions are also analized.
Ferreira, José M., Pinelas, Sandra
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