Results 1 to 10 of about 248,402 (331)
Blocks within the period of Lucas sequence
Ratio Mathematica, 2021 In this paper, we consider the periodic nature of the sequence of Lucas numbers L_n defined by the recurrence relation L_n= L_(n-1)+L_(n-2); for all n≥2; with initial condition L_0=2 and L_1=1.
Rima P. Patel, Dr. Devbhadra V. Shah
doaj +1 more source
Encryption and Decryption of the Data by Using the Terms of the Lucas Series
Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2021 The sequence, whose initial condition is 2 and 1, obtained by summing the two terms preceding it, is called the Lucas sequence. The terms of this series continue as 2, 1, 3, 4, 7, 11, 18, 29, ... respectively. The features of the Lucas sequence have been
Mehmet Duman, Merve Güney Duman
doaj +1 more source
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
Symmetric and generating functions of generalized (p,q)-numbers
Kuwait Journal of Science, 2021 In this paper, we first define new generalization for (p,q)-numbers. Considering these sequence, we give Binet's formulas and generating functions of (p,q)-Fibonacci numbers, (p,q)-Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q ...
Nabiha Saba +2 more
doaj +1 more source
A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
doaj +1 more source
On Matrix Sequence of modified Tribonacci-Lucas Numbers
MANAS: Journal of Engineering, 2022 In this paper, we define modified Tribonacci-Lucas matrix sequence and investigate its properties.
Erkan Taşdemir +2 more
doaj +1 more source
On the intersections of Fibonacci, Pell, and Lucas numbers [PDF]
, 2010 We describe how to compute the intersection of two Lucas sequences of the forms $\{U_n(P,\pm 1) \}_{n=0}^{\infty}$ or $\{V_n(P,\pm 1) \}_{n=0}^{\infty}$ with $P\in\mathbb{Z}$ that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers.
Bilu +13 more
core +2 more sources
Melham's sums for some Lucas polynomial sequences [PDF]
Notes on Number Theory and Discrete MathematicsA Lucas polynomial sequence is a pair of generalized polynomial sequences that satisfy the Lucas recurrence relation. Special cases include Fibonacci polynomials, Lucas polynomials, and Balancing polynomials.
Chan-Liang Chung, Chunmei Zhong
doaj +1 more source
Exact divisibility by powers of the integers in the Lucas sequence of the first kind
AIMS Mathematics, 2020 Lucas sequence of the first kind is an integer sequence $(U_n)_{n\geq0}$ which depends on parameters $a,b\in\mathbb{Z}$ and is defined by the recurrence relation $U_0=0$, $U_1=1$, and $U_n=aU_{n-1}+bU_{n-2}$ for $n\geq2$. In this article, we obtain exact
Kritkhajohn Onphaeng +1 more
doaj +1 more source
On members of Lucas sequences which are products of factorials [PDF]
, 2019 Here, we show that if $\{U_n\}_{n\ge 0}$ is a Lucas sequence, then the largest $n$ such that $|U_n|=m_1!m_2!\cdots m_k!$ with ...
Laishram, Shanta +2 more
core +2 more sources