Results 51 to 60 of about 903 (200)

On Generalized Jacobsthal and Jacobsthal–Lucas Numbers

Annales Mathematicae Silesianae, 2022
Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
doaj   +1 more source

Unique Properties of the Fibonacci and Lucas Sequences [PDF]

, 2017
The algebraic structure of the set of all Fibonacci-like sequences, which includes the Fibonacci and Lucas sequences, is developed, utilizing an isomorphism between this set and a subset of the 2 by 2 integer matrices.
Parry, Stephen
core   +1 more source

On Generalized Lucas Pseudoprimality of Level k

Mathematics, 2021
We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k.
Dorin Andrica, Ovidiu Bagdasar
doaj   +1 more source

Exploring Generalized $2^k$-Fibonacci Sequence: A New Family of the Fibonacci Sequence

Communications in Advanced Mathematical Sciences
The focus of this paper is to study the $2^k$–Fibonacci sequence, which is defined for all integers $2^k$, and its connections with both the Fibonacci and the Fibonacci-Lucas sequences.
Elis Gardel Costa Mesquista, Eudes Antonio Costa, Paula Maria Machado Cruz Catarino   +2 more
doaj   +1 more source

Mind the Gap: Linking Refactorings and Code Smells in Elixir

Journal of Software: Evolution and Process, Volume 38, Issue 5, May 2026.
ABSTRACT Elixir is a functional programming language increasingly used in the industry to develop scalable and fault‐tolerant concurrent systems more easily and with fewer computational resources. In previous studies, we cataloged 35 code smells and 82 refactorings tailored for this language, validating them with over 300 experienced developers ...
Lucas Vegi, Marco Túlio Valente
wiley   +1 more source

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

A Matrix Approach for Divisibility Properties of the Generalized Fibonacci Sequence

Discrete Dynamics in Nature and Society, 2013
We give divisibility properties of the generalized Fibonacci sequence by matrix methods. We also present new recursive identities for the generalized Fibonacci and Lucas sequences.
Aynur Yalçiner
doaj   +1 more source

On waiting time distribution of runs in a Fibonacci and Lucas sequences

European Journal of Science and Technology, 2021
Doğal fenomenlerin kesin bir manada tanımlanması, öngörülmesi ve anlaşılmasıyla ilgili yeni matematiksel aygıtlar geliştirme ihtiyacı giderek artmaktadır. Bu çalışmanın amacı, Fibonacci ve Lucas dizilerinin matematiksel çerçevesini modern matematiksel formüller ile desteklemek amacıyla genişletmektir.
EDABAA, Abd Anasır, BİLGİCİ, Göksal
openaire   +3 more sources

Traces of Hecke operators on Drinfeld modular forms for GL2(Fq[T])$\operatorname{GL}_2(\mathbb {F}_q[T])$

Mathematika, Volume 72, Issue 2, April 2026.
Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
wiley   +1 more source

Generalized Fibonacci and Lucas sequences and rootfinding methods [PDF]

Mathematics of Computation, 1993
Consider the sequences { u n
openaire   +1 more source