Results 11 to 20 of about 7,144 (220)
Padovan and Perrin numbers as products of two generalized Lucas numbers [PDF]
Archivum Mathematicum, 2023 Let \(P_m\) and \(E_m\) be the \(m\)th Padovan and Perrin numbers, respectively. Let \(r,s\in \mathbb{Z}\) with \(r\ge 1\) and \(s\in\{-1,1\}\), and let \(\{U_n\}_{n\ge 0}\) be the generalized Lucas sequence given by \[U_0=0,\quad U_1=1\quad\mbox{and}\quad U_{n+2}=rU_{n+1}+sU_n.\] In the paper under review, the authors give effective bounds for the ...
Adédji, Kouèssi Norbert +2 more
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Perrin Numbers That Are Concatenations of a Perrin Number and a Padovan Number in Base b
SymmetryLet (Pk)k≥0 be a Padovan sequence and (Rk)k≥0 be a Perrin sequence. Let n, m, b, and k be non-negative integers, where 2≤b≤10. In this paper, we are devoted to delving into the equations Rn=bdPm+Rk and Rn=bdRm+Pk, where d is the number of digits of Rk or Pk in base b. We show that the sets of solutions are Rn∈{R5,R6,R7,R8,R9,R10,R11,R12,R13,R14,R15,R16,
Güney Duman, Merve +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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Perrin numbers that are palindromic concatenations of two repdigits
Let $ \{P_n\}_{n\geq 0} $ be the sequence of Perrin numbers defined by $P_0=3$, $P_1=0$,$P_2=2$ and $P_{n+3}=P_{n+1}+P_{n}$ for all $n \geq 0$. In this paper, we determine all Perrin numbers that are palindromic concatenations of two repdigits.
Batte, Herbert, Kaggwa, Prosper
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k-Generalized Order-k Perrin Number Presentation by Matrix Method.
Ars Comb., 2012 In this paper, we give matrix representations of the fc-generalized order-k Perrin Numbers and we obtain relationships between these sequences and matrix. In addition, we calculate the determinant of this matrix.
Kenan Kaygisiz, Durmus Bozkurt
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On the intersection of Padovan, Perrin sequences and Pell, Pell-Lucas sequences [PDF]
, 2021 In this paper, we find all the Padovan and Perrin numbers which are Pell or Pell-Lucas ...
Rihane, Salah Eddine, Togbé, Alain
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k-Fibonacci numbers which are Padovan or Perrin numbers
Indian Journal of Pure and Applied Mathematics, 2022 Let \( \{P_m\}_{m\ge 0} \) be the sequence of Padovan numbers defined by the linear recurrence: \( P_0=P_1=P_2=1 \), and \( P_{m+3}=P_{m+1}+P_m \) for all \( m\ge 0 \). Also, let \( \{E_m\}_{m\ge 0} \) be the sequence of Perrin numbers defined by the linear recurrence: \( E_0=3,~E_1=0,~E_2=2 \), and \( E_{m+3}=E_{m+1}+E_m \) for all \( m\ge 0 ...
Salah Eddine Rihane, Alain Togbé
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Summing Formulas for Generalized Tribonacci Numbers
Universal Journal of Mathematics and Applications, 2020 In this paper, closed forms of the summation formulas for generalized Tribonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results.
Yüksel Soykan
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Common terms of k-Pell numbers and Padovan or Perrin numbers
Arabian Journal of Mathematics, 2022 AbstractLet $$k\ge 2$$ k ≥ 2 . A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence, the first k terms are $$0,\ldots ,0,1$$ 0 ,
Benedict Vasco Normenyo +2 more
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Perrin numbers that are concatenations of two repdigits
Arabian Journal of Mathematics, 2022 AbstractLet $$ (P_n)_{n\ge 0}$$ ( P n ) n ≥ 0
Herbert Batte +2 more
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