Results 261 to 270 of about 31,545 (292)

On the Completeness of the Lucas Sequence

The Fibonacci Quarterly, 1969
A sequence of positive integers is said to be complete if every positive integer is the sum of a finite number of distinct terms of the sequence. It is well-known that the Lucas sequence \(\{L_j\}\) where \(L_{n+1}=L_n+L_{n-1}\) for \(n>1\) and \(L_0=2\), \(L_1=1\) is complete. In this paper the author proves that if any term \(L_n\), where \(n>1\), is
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Palindromes in Lucas Sequences

Monatshefte f�r Mathematik, 2003
Say that \(\{w_n\}\) is a Lucas sequence if \(w_{n+2}= rw_{n+1}+sw_n\) where \(s\neq 0\) and \(r^2+4s\neq 0\). An integer is called a palindrome to base \(b\) if the base \(b\) representation of the integer is left unchanged when the digits are reversed. Let \(P(x)\) denote the number of integers \(n\leq x\) such that \(w_n\) is a base \(b\) palindrome.
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A note on the bi-periodic Fibonacci and Lucas matrix sequences

Applied Mathematics and Computation, 2018
In this paper, we introduce the bi-periodic Lucas matrix sequence and present some fundamental properties of this generalized matrix sequence. Moreover, we investigate the important relationships between the bi-periodic Fibonacci and Lucas matrix ...
Arzu Coşkun
exaly   +2 more sources

On the intersection of k-Lucas sequences and some binary sequences

Periodica Mathematica Hungarica, 2021
Lucas sequence \((L_n)\) is determined by \(L_0=2\); \(L_1=1\); \(L_n=L_{n-1}+L_{n-2}\), if \(n\ge 2\). The paper studies \(k\)-generalized \((k\ge 3)\) Lucas sequence. The sequence starts with the \(k\) terms \(0,\dots,0,2, 1\) and each term afterwards is the sum of the \(k\) preceding terms.
Salah Eddine Rihane, Alain Togbé
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CONGRUENCES CONCERNING LUCAS SEQUENCES

International Journal of Number Theory, 2014
Let p be a prime greater than 3. In this paper, by using expansions and congruences for Lucas sequences and the theory of cubic residues and cubic congruences, we establish some congruences for [Formula: see text] and [Formula: see text] modulo p, where [x] is the greatest integer not exceeding x, and m is a rational p-adic integer with m ≢ 0 ( mod p).
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On k-Lucas sequences

AIP Conference Proceedings, 2014
For positive integers n and k, the k-Lucas sequence is defined by the recurrence relation Ln+1 = kLn+Ln−1 with the initial values L0 = 2, L1 = k. The Lucas sequence and Pell-Lucas sequence are two special cases of the k-Lucas sequence. Using a matrix approach, we uncover some new facts concerning the k-Lucas sequence.
C. K. Ho, Jye-Ying Sia, Chin-Yoon Chong
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ON GENERALIZED LUCAS AND PELL-LUCAS SEQUENCES

2019
In this paper, we define the generaziled Lucas sequences and the Pell-Lucas sequences. Further we give Binet-like formulas, generating function, sums formulas and some important identities which involving the generalized Lucas and Pell-Lucas Numbers.
Tas, Zisan Kusaksiz, TAŞCI, DURSUN
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Notes on the (s, t)-Lucas and Lucas Matrix Sequences.

Ars Comb., 2008
In this article, defining the matrix extensions of the Fibonacci and Lucas numbers we start a new approach to derive formulas for some integer numbers which have appeared, often surprisingly, as answers to intricate problems, in conventional and in recreational Mathematics.
Civciv, Hacı, Türkmen, Ramazan
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On The Generalized Lucas Sequences by Hessenberg Matrices.

Ars Comb., 2010
We show that there are relationships between a generalized Lucas sequence and the permanent and determinant of some Hessenberg matrices.
Taşcı, Dursun, Haukkanen, P., Kılıç, E.   +2 more
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Lucas Sequences

2021
Masum Billal, Samin Riasat
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