Results 61 to 70 of about 237,797 (205)

Copper ratio obtained by generalizing the Fibonacci sequence

AIP Advances
In this study, we define a new generalization of the Fibonacci sequence that gives the copper ratio, and we will call it the copper Fibonacci sequence. In addition, inspired by the copper Fibonacci definition, we also define copper Lucas sequences, and ...
Engin Özkan, Hakan Akkuş
doaj   +1 more source

Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers

Journal of Mathematics, 2023
In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
doaj   +1 more source

Powers in the Lucas sequence when the index is divisible by three [PDF]

, 2011
In this paper the m-powers with m ≥ 2 included in the Lucas sequences when the index satisfies some conditions are ...
López González, M. Dolores, Rodrigo Hitos, Javier   +1 more
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On Hyperbolic Jacobsthal-Lucas Sequence

Fundamental Journal of Mathematics and Applications, 2022
In this study, we define the hyperbolic Jacobsthal-Lucas numbers and we obtain recurrence relations, Binet’s formula, generating function and the summation formulas for these numbers.
openaire   +4 more sources

On a unified approach to homogeneous second-order linear difference equations with constant coefficients and some applications

Special Matrices
In this article, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory.
Kaddoura Issam, Mourad Bassam
doaj   +1 more source

On Lucas Sequences Computation

Int'l J. of Communications, Network and System Sciences, 2010
This paper introduces an improvement to a currently published algorithm to compute both Lucas "sister" sequences Vk and Uk. The proposed algorithm uses Lucas sequence properties to improve the running time by about 20% over the algorithm published in [1].
openaire   +2 more sources

On the complex factorization of the Lucas sequence

Applied Mathematics Letters, 2011
In this paper, firstly we present a connection between determinants of tridiagonal matrices and the Lucas sequence. Secondly, we obtain the complex factorization of Lucas sequence by considering how the Lucas sequence can be connected to Chebyshev polynomials by determinants of a sequence of matrices.
Durmuş Bozkurt, Ş. Burcu Bozkurt, Fatih Yilmaz   +2 more
openaire   +2 more sources

On the emergence of the Quanta Prime sequence

Arab Journal of Basic and Applied Sciences
This paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications.
Moustafa Ibrahim
doaj   +1 more source

The class of Lucas-Lehmer polynomials [PDF]

Rendiconti di Matematica e delle Sue Applicazioni, 2016
In this paper we introduce a new sequence of polynomials, which follow the same recursive rule of the well-known Lucas-Lehmer integer sequence. We show the most important properties of this sequence, relating them to the Chebyshev polynomials of the ...
Pierluigi Vellucci, Alberto Maria Bersani   +1 more
doaj  

Lucas Numbers and Cryptography [PDF]

, 2012
We know that the Fibonacci numbers are the numbers from Fibonacci sequence. It was discovered by Leonardo de Fibonacci de Pisa. The Fibonacci series was derived from the solution to a problem about rabbits.
Thokchom, Chhatrajit Singh
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