Results 81 to 90 of about 616 (205)
Narayana Numbers With Zeckendorf Partition in Two Terms
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The Narayan’s cow sequence starts with the terms 1, 1, and 1. Each subsequent term is obtained as the sum of the previous term and the term three places before. A term of this sequence is called a Narayana number. The mathematician Zeckendorf proved that every positive integer has a unique decomposition into a sum of distinct and nonconsecutive ...
Japhet Odjoumani +2 more
wiley +1 more source
Primes in Fibonacci n-step and Lucas n-step Sequences [PDF]
, 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
Fibonacci and Lucas sequences at negative indices [PDF]
, 2016 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.
Akyüz, Zeynep, Halıcı, Serpil
core
Bi‐Starlike Function of Complex Order Involving Rabotnov Function Associated With Telephone Numbers
Journal of Mathematics, Volume 2025, Issue 1, 2025.Telephone numbers defined through the recurrence relation Qn=Qn−1+n−1Qn−2 for n ≥ 2, with initial values of Q0=Q1=1. The study of such numbers has led to the establishment of various classes of analytic functions associated with them. In this paper, we establish two new subclasses of bi‐convex and bi‐starlike functions of complex order in the open unit
Sa’ud Al-Sa’di +3 more
wiley +1 more source
On the Existence of Solutions of Diophantine Equations Related to Subbalancing Numbers
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this paper, we introduce a new sequence of subbalancing numbers by considering balancing numbers as the values of D in the Diophantine equations provided by subbalancing numbers. For this, first we prove that when the values of the positive integer D are chosen as balancing numbers, there exist integer solutions of the Diophantine equations that ...
Selin Sarı +2 more
wiley +1 more source
Q-Analogues of biperiodic fibonacci and lucas sedenions [PDF]
, 2021 Quantum calculus has an important areas in many areas such as number theory, physics and mathematics. In this paper, by taking some useful notations from quantum calculus, we define the biperiodic Fibonacci and Lucas sedenions based on a q-parameter ...
Köme, Sure, Gün, Hafize
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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
4x4 Symmetric Toeplitz Tridiagonal Fibonacci and Lucas Matrices [PDF]
, 2021 Yüksek Lisans TeziBu çalışmada, Fibonacci ve Lucas dizilerinden ve sıralı ikili elemanlara sahip 4x4 mertebeli simetrik Toeplitz üç bant matrislerin pozitif tamsayı kuvvetlerinin Fibonacci veya Lucas matrisleri olduğu gösterilerek bu matrislerin ...
Aksoy, Muaz
core +1 more source
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
doaj +1 more source
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