A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a ...
Hasan Gökbaş, Mohammad W. Alomari
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Repdigits as Products of Consecutive Pell or Pell–Lucas Numbers
Iranian Journal of Mathematical Sciences and InformaticsSummary: A positive integer is called a repdigit if it has only one distinct digit in its decimal expansion. In this paper, we find all repdigits that are products of consecutive Pell or Pell-Lucas numbers. This paper continues previous work which dealt with finding occurrences of repdigits in the Pell and Pell-Lucas sequences.
Bravo, Eric F., Bravo, Jhon J.
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Genetic erosion in domesticated barley and a hypothesis of a North African centre of diversity
Ecology and Evolution, Volume 14, Issue 8, August 2024.Barley cultivated 6 millennia ago was more diverse than extant cultivars and landraces. Private variants and chloroplast haplotypes indicate strong genetic erosion in North Africa and link together ancient barley, extant Ethiopian landraces and a rudimentary wild population of Cyrenaica.
Peter Civáň +6 more
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Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials
Turkish Journal of Analysis and Number Theory, 2019 In this paper, we introduce a operator in order to derive a new generating functions of modified k- Pell numbers, Gaussian modified Pell numbers. By making use of the operator defined in this paper, we give some new generating functions for Bivariate ...
S. Boughaba +2 more
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Convolutions of the generalized Pell and Pell-Lucas numbers
Filomat, 2016 We consider the convolution of the generalized Pell numbers-P(s) n,m and the convolution of the generalized Pell-Lucas numbers-Q(s) n,m. For s = 0, the sequence P(0) n,m represents the generalized Pell numbers Pn;m, and the sequence Q(0) n,m represents the generalized Pell-Lucas numbers Qn,m ([1], [2]). For m = 2 and s = 0, the numbers P(0)
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Pell and Pell-Lucas numbers as sums of two Jacobsthal numbers
, 2022 First ...
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Mulatu Numbers as Products of Three Generalized Lucas Numbers
Mathematica PannonicaLet 𝑀𝑘 be the 𝑘-th Mulatu number. Let 𝑟, 𝑠 be non-zero integers with 𝑟 ≥ 1 and 𝑠 ∈ {−1, 1}, let {𝑈𝑛}𝑛≥0 be the generalized Lucas sequence and {𝑉𝑛}𝑛≥0 its companion given respectively by 𝑈𝑛+2 = 𝑟𝑈𝑛+1 + 𝑠𝑈𝑛 and 𝑉𝑛+2 = 𝑟𝑉𝑛+1 + 𝑠𝑉𝑛, with 𝑈0 = 0, 𝑈1 = 1, 𝑉0 =
K. N. Adédji +2 more
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Accidental Intraoperative Mandibular Fracture in a Third Molar Surgery: When Surgical Skills Are Mandatory in the Face of Empiricism. [PDF]
Case Rep Dent, 2023 Pinho JNA +5 more
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On $X$-coordinates of Pell equations which are repdigits
, 2017 Let $b\ge 2$ be a given integer. In this paper, we show that there only finitely many positive integers $d$ which are not squares, such that the Pell equation $X^2-dY^2=1$ has two positive integer solutions $(X,Y)$ with the property that their $X ...
Faye, Bernadette, Luca, Florian
core
Pell and Pell-Lucas numbers as sums of three repdigits
, 2020 Same work has been study by another ...
Bhoi, Kisan +2 more
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