Results 241 to 250 of about 255,828 (280)

Two generalizations of Lucas sequence

Applied Mathematics and Computation, 2014
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Goksal Bilgici
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On Primes in Lucas Sequences

The Fibonacci Quarterly, 2015
Consider the Lucas sequence u(a, b) = (un(a, b)) and the companion Lucas sequence v(a, b) = (vn(a, b)) which both satisfy the second order recursion relation wn+2 = awn+1 − bwn with initial terms u0 = 0, u1 = 1, and v0 = 2, v1 = a, respectively. We give both necessary and sufficient tests and also necessary tests for the primality of |un| and |vn|. For
Křížek, M. (Michal), Somer, L.
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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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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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(Verifiable) Delay Functions from Lucas Sequences

2023
Lucas sequences are constant-recursive integer sequences with a long history of applications in cryptography, both in the design of cryptographic schemes and cryptanalysis. In this work, we study the sequential hardness of computing Lucas sequences over an RSA modulus. First, we show that modular Lucas sequences are at least as sequentially hard as the
Charlotte Hoffmann, Pavel Hubáček, Chethan Kamath, Tomáš Krňák   +3 more
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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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Tribonacci-Lucas Sequence Spaces

2022
In this work, we basically define new sequence spaces using Tribonacci-Lucas numbers. Then, we give some inclusion relations by examining some topological properties of these spaces. We also characterize some matrix classes by calculating the Köthe-Toeplitz duals of our space.
KARAKAŞ, Murat, ŞEVİK, Uğurcan
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Primefree shifted Lucas sequences

Acta Arithmetica, 2015
Summary: We say a sequence \(\mathcal S=(s_n)_{n\geq 0}\) is primefree if \(|s_n|\) is not prime for all \(n\geq 0\), and to rule out trivial situations, we require that no single prime divides all terms of \(\mathcal S\). In this article, we focus on the particular Lucas sequences of the first kind, \(\mathcal U_a=(u_n)_{n\geq 0}\), defined by \[ u_0 ...
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Lucas Sequences

2021
Masum Billal, Samin Riasat
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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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