Results 151 to 160 of about 254,724 (185)
Some of the next articles are maybe not open access.
Tribonacci-Lucas Sequence Spaces
2022In 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
openaire +1 more source
Primefree shifted Lucas sequences
Acta Arithmetica, 2015Summary: 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 ...
openaire +1 more source
ON GENERALIZED LUCAS AND PELL-LUCAS SEQUENCES
2019In 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
openaire +1 more source
Shifting Lucas Sequences Away from Primes
Summary: We strengthen a result of Jones by showing that for any positive integer \(P\), the Lucas sequence \((U_n)_n\) defined by \(U_0 = 0\), \(U_1 = 1\), \(U_n=P \cdot U_{n -1} + U_{n - 2}\) can be translated by a positive integer \(K(P)\) such that the shifted sequence with general term \(U_n + K(P)\) contains no primes, nor terms one unit away ...Ismailescu, Dan +4 more
openaire +2 more sources
Mersenne Numbers in Generalized Lucas Sequences
Proceedings of the Bulgarian Academy of SciencesLet $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer.
Altassan, Alaa, ALAN, Murat
openaire +2 more sources
Lucas Sequences in Primality Testing
2014Prime or composite? This classification determines whether or not integers can be used in digital security. One such way to begin testing an integers primality is with the Fermat test, which says that if n is a prime number and a is an integer then an-1 1 mod n.
openaire +1 more source