Results 1 to 10 of about 8,607,312 (168)
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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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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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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Powers of Two as Sums of Two Padovan Numbers
Integers, 2018 See the abstract in the attached pdf.
Ana Cecilia García Lomelí +1 more
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Padovan numbers that are concatenations of two distinct repdigits [PDF]
Mathematica Slovaca, 2020 Abstract Let ( P n ) n ≥0 be the sequence of Padovan numbers defined by P
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On Doubled and Quadrupled Fibonacci Type Sequences
Annales Mathematicae SilesianaeIn this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled ...
Yilmaz Nur Şeyma +3 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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On the problem of Pillai with Padovan numbers and powers of 3 [PDF]
Studia Scientiarum Mathematicarum Hungarica, 2019 Abstract Let {P n}n≥0 be the sequence of Padovan numbers defined by P0 = 0, P1 = 1, P2 = 1, and Pn+3 = Pn+1 + Pn for all n ≥ 0. In this paper, we find all integers c admitting at least two representations as a difference between a Padovan number and a power of 3.
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Padovan numbers which are concatenations of three Padovan or Perrin numbers
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 \[ P_{k}=10^{d+l}P_{m}+10^{l}P_{n}+P_{r} \] and \[ P_{k}=10^{d+l}R_{m}+10^{l}R_{n}+R_{r} \] where k, m, n, r, d and l are positive integers satisfying n ≤ m.
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The X -coordinates of Pell equations and Padovan numbers
TURKISH JOURNAL OF MATHEMATICS, 2019 Summary: In this paper, we show that there is at most one value of the positive integer \(X\) participating in the Pell equation \(X^2-dY^2=k\), where \(k\in\{\pm1,\pm4\}\), which is a Padovan number, with a few exceptions that we completely characterize.
Salah Eddine RIHANE +2 more
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