Results 91 to 100 of about 903 (200)
The Third Order Jacobsthal Octonions: Some Combinatorial Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways.
Cerda-Morales Gamaliel
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Fibonacci and Lucas sequences at negative indices
, 2014 This study investigate the Fibonacci and Lucas sequences at neg- ative indices. In this paper we give the formulas of F????(nk+r) and L????(nk+r) depending on whether the indices are odd or even. For this purpose we con- sider a special matrix and we give various combinatorial identities related with the Fibonacci and Lucas sequences by using the ...
Halıcı, Serpil, Akyüz, Zeynep
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A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a ...
Hasan Gökbaş, Mohammad W. Alomari
wiley +1 more source
On the Periods of Biperiodic Fibonacci and Biperiodic Lucas Numbers
Discrete Dynamics in Nature and Society, 2016 This paper is concerned with periods of Biperiodic Fibonacci and Biperiodic Lucas sequences taken as modulo prime and prime power. By using Fermat’s little theorem, quadratic reciprocity, many results are obtained.
Dursun Tascı, Gul Ozkan Kızılırmak
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Orbit quotients in the radical ring of multiplicative arithmetic functions [PDF]
Mathematica BohemicaWe extend the role of algebraic structures to the study of multiplicative arithmetic functions by associating the corresponding radical ring and a left-group action with the quasi-field (two-sided brace) of multiplicative arithmetic functions.
Emil Daniel Schwab
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Strong divisibility sequences and sieve methods
Mathematika, Volume 70, Issue 4, October 2024.Abstract We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods.
Tim Browning, Matteo Verzobio
wiley +1 more source
A new generalization of Fibonacci and Lucas type sedenions
, 2022 In this paper, by using the q-integer, we introduce a new generalization of Fibonacci and Lucas type sedenions called q-Fibonacci and q-Lucas sedenions.
Can Kızılateş, Selihan Kirlak
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A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
Bahar Kuloğlu
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Primes in Fibonacci n-step and Lucas n-step Sequences
, 2005 We search for primes in the Fibonacci n-step and Lucas n-step sequences, which are the natural generalizations of the Fibonacci and Lucas numbers. While the Fibonacci n-step sequences are nearly devoid of primes, the Lucas n-step sequences are prime-rich.
Tony D. Noe, Jonathan Vos Post
core
Weak Pseudoprimality Associated with the Generalized Lucas Sequences
, 2022 Pseudoprimes are composite integers which share properties of the prime numbers, and they have applications in many areas, as, for example, in public-key cryptography.
Andrica, D. +5 more
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