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On quaternion‐Gaussian Lucas numbers

Mathematical Methods in the Applied Sciences, 2020
In this study, we have considered Gaussian Lucas numbers and given the properties of these numbers. Then, we have defined the quaternions that accept these numbers as coefficients. We have examined whether the numbers defined provide some identities for quaternions in the literature.
Serpil Halici, Halıcı, Serpil
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New recurrences on Pell numbers, Pell-Lucas numbers, Jacobsthal numbers, and Jacobsthal-Lucas numbers

Chaos, Solitons and Fractals, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Songul Çelik, Engin Özkan
exaly   +2 more sources

On Square Pseudo-Lucas Numbers

Canadian Mathematical Bulletin, 1978
J. H. E. Cohn (1) has shown thatare the only square Fibonacci numbers in the set of Fibonacci numbers defined byIf n is a positive integer, we shall call the numbers defined by(1)pseudo-Lucas numbers.
A. Eswarathasan
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Mersenne Numbers in Generalized Lucas Sequences

Proceedings of the Bulgarian Academy of Sciences
Let $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer.
ALAN, Murat, Altassan, Alaa
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Lucas Numbers and Determinants

Integers, 2012
Abstract.In this article, we present two infinite dimensional matrices whose entries are recursively defined, and show that the sequence of their principal minors form the Lucas sequence, that ...
Alireza Moghaddamfar, Hadiseh Tajbakhsh
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Optimization by k-Lucas numbers

Applied Mathematics and Computation, 2008
The well-known Fibonacci search method to find the maximum point of unimodal functions on closed intervals is modified by using \(k\)-Lucas numbers. This makes the Fibonacci search method more effective and improves an earlier algorithm by \textit{B. Yildiz} and \textit{E. Karaduman} [Appl. Math. Comput. 143, No. 2--3, 523--551 (2003; Zbl 1041.11013)].
Ali Demir, Nese Ömür, Yucel Turker Ulutas   +2 more
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On Concatenations of Fibonacci and Lucas Numbers

Bulletin of the Iranian Mathematical Society, 2022
Let \( (F_n)_{n\ge 0} \) and \( (L_n)_{n\ge 0} \) be the usual Fibonacci and Lucas sequences defined respectively by the linear recurrence relations: \( F_0=0 \), \( F_1=1 \), \( F_{n+2}=F_{n+1}+F_n \) and \( L_0=2 \), \( L_1=1 \), \( L_{n+2}=L_{n+1}+L_n \) for all \( n\ge 0 \).
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Lucas' number is finally up

Journal of Philosophical Logic, 1982
Discussion de l'argumentation de J. R. Lucas suivant laquelle les etres humains ne peuvent etre des machines ("Minds, Machines and Godel", Philosophy, 36, 1961, p. 120-124). L'A. montre que l'argument de Lucas suivant lequel il n'est pas une machine repose sur une premisse erronee: suivant l'A., Lucas est donc lui-meme une machine.
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Perfect fibonacci and lucas numbers

Rendiconti del Circolo Matematico di Palermo, 2000
Using elementary means, the author shows that no Fibonacci or Lucas number is perfect.
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Fibonacci and Lucas Numbers

2021
In the literature, the Fibonacci numbers are usually denoted by \(F_n\), but this symbol is already reserved for the Fermat numbers in this book. So we will denote them by \(K_n\). The sequence of Fibonacci numbers \(\,\,(K_n)_{n=0}^\infty \,\,\) starts with \(K_0=0\) and \(K_1=1\) and satisfies the recurrence.
Michal Křížek, Lawrence Somer, Alena Šolcová   +2 more
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