Results 21 to 30 of about 648 (170)
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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Padovan numbers that are concatenations of a Padovan number and a Perrin number
Periodica Mathematica HungaricaThe sequence of Padovan numbers defined by \(P_0 = P_1 = P_2 = 1; P_k = P_{k-2} + P_{k-3}\). The sequence of Perrin numbers defined by \(R_0 = 3, R_1 = 0, R_2 = 2; R_k = R_{k-2} + R_{k-3}\). The author determines all Padovan numbers which can be written as concatenations of a Padovan number and a Perrin number. Baker's method and Davenport reduction is
Güney Duman, Merve +2 more
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Padovan numbers as sums over partitions into odd parts
Journal of Inequalities and Applications, 2016 Recently it was shown that the Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. In this paper, we introduce a similar representation for the Padovan numbers. As a corollary, we derive
Cristina Ballantine, Mircea Merca
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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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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.
Mahadi Ddamulira, Ddamulira, Mahadi
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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
Odjoumani, Japhet +2 more
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A Study on Generalized Jacobsthal-Padovan Numbers
Earthline Journal of Mathematical Sciences, 2020 In this paper, we investigate the generalized Jacobsthal-Padovan sequences and we deal with, in detail, four special cases, namely, Jacobsthal-Padovan, Jacobsthal-Perrin, adjusted Jacobsthal-Padovan and modified Jacobsthal-Padovan sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these ...
Yüksel Soykan
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A Historical Analysis of The Padovan Sequence
International Journal of Trends in Mathematics Education Research, 2020 In the present text, we present some possibilities to formalize the mathematical content and a historical context, referring to a numerical sequence of linear and recurrent form, known as Sequence of Padovan or Cordonnier.
Renata Passos Machado Vieira +2 more
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Padovan numbers which are palindromic concatenations of two distinct repdigits. [PDF]
Rev R Acad Cienc Exactas Fis Nat A Mat, 2021 International audienceIn this paper we determine all Padovan numbers that are palindromic concatenations of two ...
Chalebgwa TP, Ddamulira M.
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Combinatorial Identities for the Padovan Numbers
The Fibonacci Quarterly, 2019 We interpret the Padovan numbers combinatorially by having them count the number of tilings of an n-strip using dominoes and triominoes. Using this interpretation, we develop a collection of identities satisfied by the sequence of Padovan ...
Tedford, Steven J.
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