Results 31 to 40 of about 2,231,198 (301)
Mersenne-Horadam identities using generating functions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
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On Bicomplex Jacobsthal-Lucas Numbers
Journal of Mathematical Sciences and Modelling, 2020 In this study we introduced a sequence of bicomplex numbers whose coefficients are chosen from the sequence of Jacobsthal-Lucas numbers. We also present some identities about the known some fundamental identities such as the Cassini's, Catalan's and ...
Serpil Halıcı
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Some Polynomial Sequence Relations
Mathematics, 2019 We give some polynomial sequence relations that are generalizations of the Sury-type identities. We provide two proofs, one based on an elementary identity and the other using the method of generating functions.
Chan-Liang Chung
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Binomial Coefficients and Lucas Sequences
Journal of Number Theory, 2002 Let sequences \(\{u_n\}_{n\geq 0}\) and \(\{v_n\}_{n\geq 0}\) be defined by \(u_n= \frac{a^n-b^n}{a-b}\), \(v_n= a^n+b^n\) where \(a,b\) are integers such that \(a>|b|\). (Such sequences are Lucas sequences such that the associated quadratic polynomial has integer roots.
Flammenkamp, Achim, Luca, Florian
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On Lucas Sequences Computation
Int'l J. of Communications, Network and System Sciences, 2010 This paper introduces an improvement to a currently published algorithm to compute both Lucas "sister" sequences Vk and Uk. The proposed algorithm uses Lucas sequence properties to improve the running time by about 20% over the algorithm published in [1].
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On arithmetic progressions in Lucas sequences
J. Integer Seq., 2017 In this paper, we consider arithmetic progressions contained in Lucas sequences of first and second kind. We prove that for almost all sequences, there are only finitely many and their number can be effectively bounded. We also show that there are only a few sequences which contain infinitely many and one can explicitly list both the sequences and the ...
Lajos Hajdu +2 more
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Transcripts enriched in codons that trigger P‐site tRNA‐mediated mRNA decay possess stable mRNA
FEBS Open Bio, EarlyView.PTMD codons were first described by Mendel et al. as mediators of an mRNA decay pathway dependent on the human protein CNOT3, homologous to yeast Not5. Our findings confirm that PTMD codons destabilize transcripts; however, unlike in yeast, the human pathway specifically targets and slightly destabilizes primarily stable mRNAs.
Rodolfo Lopes Carneiro +1 more
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Repdigits in k-Lucas sequences
Proceedings - Mathematical Sciences, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bravo, Jhon J., Luca, Florian
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ATZ‐1 promotes DNA replication efficiency to maintain normal meiotic function
FEBS Open Bio, EarlyView.Absence of ATZ‐1 interferes with meiotic DNA replication and cell cycle function via CHK‐1. This causes downstream defects associated with DNA damage and genomic integrity. Taken together, this study suggests that ATZ‐1 influences DNA replication efficiency and cell cycle function to maintain normal meiotic function.
Taylin E. Gourley +5 more
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On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
Karpatsʹkì Matematičnì Publìkacìï, 2021 The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
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