Results 1 to 10 of about 145,495 (205)
Integers represented by Lucas sequences [PDF]
arXivIn this paper we study the sets of integers which are $n$-th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for $n$ sufficiently large. We also develop bounds on the growth order of the terms of Lucas sequences that are independent of the parameters of the sequence, which is a new ...
Lajos Hajdu, R. Tijdeman
arxiv +4 more sources
Lucas sequences and repdigits [PDF]
Mathematica Bohemica, 2022 Let $(G_n)_{n \geq1}$ be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are $\{U_n\}$ and $\{V_n\}$, respectively.
Hayder Raheem Hashim, Szabolcs Tengely
doaj +3 more sources
The Lucas Numbers and other Gibonacci Sequences mod $m$ [PDF]
arXiv, 2014 We study Gibonacci sequences mod $m$, giving special attention to the Lucas numbers. It is known which $m$ have the property that the Fibonacci sequence contains all residues mod $m$. When $m$ has this property, we say that the Fibonacci sequence is complete mod $m$.
Jeremiah Southwick
arxiv +3 more sources
Log-concavity of Lucas Sequences of first kind [PDF]
arXiv, 2011 In these notes we address the study of the log-concave operator acting on Lucas Sequences of first kind. We will find for which initial values a generic Lucas sequence is log-concave, and using this we show when the same sequence is infinite log-concave.
P Giacomelli
arxiv +3 more sources
On a divisibility relation for Lucas sequences
Journal of Number Theory, 2016 In this note, we study the divisibility relation $U_m\mid U_{n+k}^s-U_n^s$, where ${\bf U}:=\{U_n\}_{n\ge 0}$ is the Lucas sequence of characteristic polynomial $x^2-ax\pm 1$ and $k,m,n,s$ are positive integers.
Yuri Bilu +4 more
openalex +8 more sources
The GCD Sequences of the Altered Lucas Sequences [PDF]
Annales Mathematicae Silesianae, 2020 In this study, we give two sequences {L+n}n≥1 and {L−n}n≥1 derived by altering the Lucas numbers with {±1, ±3}, terms of which are called as altered Lucas numbers.
Koken Fikri
doaj +2 more sources
Some results on average of Fibonacci and Lucas sequences [PDF]
arXiv, 2020 In this paper, we discuss about some results on average of Fibonacci and Lucas sequences that may be found in the OEIS code A111035.
Daniel Yaqubi, Amirali Fatehizadeh
arxiv +3 more sources
Tribonacci and Tribonacci-Lucas Matrix Sequences with Negative Subscripts [PDF]
arXiv, 2018 In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences with negative indices and investigate their properties.
Yüksel Soykan
arxiv +3 more sources
A Digital Image Confidentiality Scheme Based on Pseudo-Quantum Chaos and Lucas Sequence [PDF]
Entropy, 2020 Several secure image encryption systems have been researched and formed by chaotic mechanisms in current decades. This work recommends an innovative quantum color image encryption method focused on the Lucas series-based substitution box to enhance the ...
Khushbu Khalid Butt +3 more
doaj +2 more sources
A generalization of Lucas polynomial sequence
Discrete Applied Mathematics, 2008 In this paper, we obtain a generalized Lucas polynomial sequence from the lattice paths for the Delannoy numbers by allowing weights on the steps (1,0),(0,1) and (1,1). These weighted lattice paths lead us to a combinatorial interpretation for such a Lucas polynomial sequence. The concept of Riordan arrays is extensively used throughout this paper.
Gi‐Sang Cheon +2 more
openalex +3 more sources