A Study on the k-Mersenne and k-Mersenne-Lucas Sequences

In this study, we examine an application of $k-$Mersenne and $k-$Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of $k-$Mersenne and $k-$Mersenne-Lucas sequences have terms according to different v...

Full description

Bibliographic Details
Published in:	Universal Journal of Mathematics and Applications
Main Authors:	Mine Uysal, Hakan Akkuş, Bayram Şen, Engin Özkan
Format:	Article
Language:	English
Published:	Emrah Evren KARA 2025-03-01
Subjects:	catalan numbers fibonacci numbers generating functions hankel transform $k$-mersenne sequences $k$-mersenne-lucas sequences
Online Access:	https://dergipark.org.tr/en/download/article-file/4284061

Similar Items

On the Split Mersenne and Mersenne-Lucas Hybrid Quaternions
by: B. Malini Devi, et al.
Published: (2023-03-01)

On New Sequences of $p$-Binomial and Catalan Transforms of the $k$-Mersenne Numbers and Associated Generating Functions
by: Kalika Prasad, et al.
Published: (2025-06-01)

The generalized order (k,t)-Mersenne sequences in groups
by: E. Mehraban, et al.
Published: (2024-05-01)

Fermat and Mersenne numbers in $k$-Pell sequence
by: B. Normenyo, et al.
Published: (2021-12-01)

Mersenne-Horadam identities using generating functions
by: R. Frontczak, et al.
Published: (2020-06-01)

The First Study of Mersenne--Leonardo Sequence
by: Paula Maria Machado Cruz Catarino, et al.
Published: (2025-03-01)

A New Approach to k-Jacobsthal Lucas Sequences
by: Hakan Akkuş, et al.
Published: (2021-08-01)

On generalized bihyperbolic Mersenne numbers
by: Dorota Bród, et al.
Published: (2024-04-01)

Mersenne Matrix Operator and Its Application in $p-$Summable Sequence Space
by: Sezer Erdem, et al.
Published: (2024-03-01)

Mersenne version of Brocard-Ramanujan equation
by: Ayşe Nalli, et al.
Published: (2023-04-01)

Os números híbridos de k-Mersenne e k-Oresme
by: Milena Carolina dos Santos Mangueira, et al.
Published: (2021-12-01)

Affine–Hill cipher from Hadamard-type Fibonacci–Mersenne and Fibonacci-balancing p-sequences
by: Elahe Mehraban, et al.
Published: (2025-09-01)

On the Eight Levels theorem and applications towards Lucas-Lehmer primality test for Mersenne primes, I
by: Moustafa Ibrahim
Published: (2023-12-01)

Some new properties of hyperbolic k-Fibonacci and k-Lucas octonions
by: A. D. Godase
Published: (2024-03-01)

The emergence of the Mersenne Star: a new geometry of prime numbers bridging physics and artificial general intelligence
by: Moustafa Ibrahim
Published: (2025-12-01)

Boolean Hypercubes, Mersenne Numbers, and the Collatz Conjecture
by: Ramon Carbó Dorca
Published: (2020-12-01)

MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD
by: N. A. Balonin, et al.
Published: (2014-05-01)

Números híbridos de Mersenne
by: Milena Carolina dos Santos Mangueira, et al.
Published: (2020-07-01)

On Mersenne Numbers and their Bihyperbolic Generalizations
by: Bród Dorota, et al.
Published: (2024-08-01)

HMNT: Hash Function Based on New Mersenne Number Transform
by: Ali Maetouq, et al.
Published: (2020-01-01)

New sequences from the generalized Pell p−numbers and mersenne numbers and their application in cryptography
by: Elahe Mehraban, et al.
Published: (2024-04-01)

A study on the number of edges of some families of graphs and generalized Mersenne numbers
by: K.G. Sreekumar, et al.
Published: (2022-06-01)

Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions
by: Ramírez José L.
Published: (2015-06-01)

COMPARATIVE STUDY BETWEEN A NOVEL DETERMINISTIC TEST FOR MERSENNE PRIMES AND THE WELL-KNOWN PRIMALITY TESTS
by: Yahia Awad, et al.
Published: (2023-10-01)

DETERMINANTAL IDENTITIES FOR k LUCAS SEQUENCE
by: Ashok Dnyandeo Godase, et al.
Published: (2016-07-01)

Development of modified RSA algorithm using fixed mersenne prime numbers for medical ultrasound imaging instrumentation
by: Seung-Hyeok Shin, et al.
Published: (2019-10-01)

Properties of Generalized Bronze Fibonacci Sequences and Their Hyperbolic Quaternions
by: Engin Özkan, et al.
Published: (2024-12-01)

A MATEMÁTICA NA METAFÍSICA CARTESIANA: UMA DISPUTA ENTRE DESCARTES E MERSENNE
by: Suellen Caroline Teixeira
Published: (2024-08-01)

Sobre o ceticismo moderado de Mersenne, Gassendi e Hume
by: Flávio Miguel de Oliveira Zimmermann
Published: (2009-06-01)

Minimality Conditions Equivalent to the Finitude of Fermat and Mersenne Primes
by: Menachem Shlossberg
Published: (2023-05-01)

On the k-Fibonacci and k-Lucas spinors
by: Munesh Kumari, et al.
Published: (2023-05-01)

Partitions of numbers and the algebraic principle of Mersenne, Fermat and even perfect numbers
by: A. M. S. Ramasamy
Published: (2024-11-01)

On the solution of the exponential Diophantine equation 2x+m2y=z2, for any positive integer m
by: Mridul Dutta, et al.
Published: (2023-12-01)

Generalizing the eight levels theorem: a journey to Mersenne prime discoveries and new polynomial classes
by: Moustafa Ibrahim
Published: (2024-12-01)

A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers
by: Yunlan Wei, et al.
Published: (2019-09-01)

On the emergence of the Quanta Prime sequence
by: Moustafa Ibrahim
Published: (2025-12-01)

Marin Mersenne (1588-1648): apologética tradicional cristiana frente a la crisis religiosa de 1623
by: Carlos Gómez
Published: (1997-01-01)

An Alternating Sum of Fibonacci and Lucas Numbers of Order <i>k</i>
by: Spiros D. Dafnis, et al.
Published: (2020-09-01)

On the Lichtenberg hybrid quaternions
by: Morales Gamaliel
Published: (2025-01-01)

Efficient and Constant Time Modular Reduction With Generalized Mersenne Primes
by: Serdar S. Erdem, et al.
Published: (2024-01-01)