Results 21 to 30 of about 1,194,375 (170)
On Gaussian Jacobsthal-Padovan Numbers
Cumhuriyet Science Journal, 2022 Gaussian Jacobsthal-Padovan numbers have been the central focus of this paper and firstly this number sequence has defined. Later, we have given the proof of the generating function of the Gaussian Jacobsthal-Padovan sequence.
Nusret Karaaslan
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Padovan numbers which are concatenations of three Padovan or Perrin numbers [PDF]
Notes on Number Theory and Discrete MathematicsThis paper presents all Padovan numbers that can be written as the concatenation of three Padovan or Perrin numbers under a certain constraint. Namely, we consider the Diophantine equations Pₜ=10ᵈ⁺ˡPₘ+10ˡPₙ+Pᵣ and Pₜ=10ᵈ⁺ˡRₘ+10ˡRₙ+Rᵣ, where k,m,n,r,d and
Fatih Erduvan
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The Hybrid Numbers of Padovan and Some Identities
Annales Mathematicae Silesianae, 2020 In this article, we will define Padovan’s hybrid numbers, based on the new noncommutative numbering system studied by Özdemir ([7]). Such a system that is a set involving complex, hyperbolic and dual numbers.
Mangueira Milena Carolina dos Santos +3 more
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On Generalized Padovan Numbers
, 2021 In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences.
Soykan, Yüksel
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New Types of Distance Padovan Sequences via Decomposition Technique
Applied Sciences (Switzerland), 2022 In this paper, we introduce new kinds of generalized Padovan sequences and study their properties using number decomposition techniques. In particular, we consider three types of generalized Padovan sequences defined by the same recurrence equation with ...
Małgorzata Wołowiec-Musiał +2 more
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Axioms, 2022 There is ongoing research into combinatorial methods and approaches for linear and recurrent sequences. Using the notion of a board defined for the Fibonacci sequence, this work introduces the Padovan sequence combinatorial approach.
Paula Catarino +1 more
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Padovan numbers as difference of two repdigits
Indian Journal of Pure and Applied Mathematics, 2023 In the paper under review, the author determines all the Padovan numbers that are expressible as a difference of two repdigits. To prove the main result, the authors uses a clever combination of techniques in Diophantine number theory, the usual properties of Padovan sequence, Baker's theory for nonzero lower bounds for linear forms in logarithms of ...
Duman, Merve Guney +3 more
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Generalized Pell-Padovan Numbers
Asian Journal of Advanced Research and Reports, 2020 In this paper, we investigate the generalized Pell-Padovan sequences and we deal with, in detail, four special cases, namely, Pell-Padovan, Pell-Perrin, third order Fibonacci-Pell and third order Lucas-Pell sequences. We present Binet’s formulas, generating functions, Simson formulas and the summation formulas for these sequences.
Yüksel Soykan, Soykan, Yüksel
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On the Two-Term Zeckendorf Representations of the Padovan and Perrin Sequences
Journal of Applied MathematicsIn this paper, we completely solve the Diophantine equations Pm=Fn+Fk and Em=Fn+Fk under the condition n≥k+2≥4, where Pm is the m-th Padovan number, Em is the m-th Perrin number, and Fk is the k-th Fibonacci number.
Awaou Lare Ousseni +3 more
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The Padovan numbers of the form 6a ± 6 b ± 6 c
Revista Integración, 2023 Let (Pn)n>0 be the Padovan sequence given by P0 = 0, P1 = P2 = 1 and the recurrence formula Pn+3 = Pn+1 + Pn for all n > 0. In this note, we completely solve the Diophantine equation Pn = 6a ± 6b ± 6c in non-negative integers (n, a, b, c) with a > b > c
Ana Cecilia García Lomelí +1 more
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