Results 11 to 20 of about 6,644 (181)
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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Padovan and Perrin numbers as products of two generalized Lucas numbers
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 and distinct repdigits [PDF]
, 2020 We determine all Perrin numbers that are concatenations of two repdigits.
Mahadi Ddamulira, Toboka Chalebgwa
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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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Perrin numbers that are concatenations of two distinct repdigits [PDF]
, 2021 Let $ (P_n)_{n\ge 0}$ be the sequence of Perrin numbers defined by ternary relation $ P_0=3 $, $ P_1=0 $, $ P_2=2 $, and $ P_{n+3}=P_{n+1}+P_n $ for all $ n\ge 0 $. In this paper, we use Baker's theory for nonzero linear forms in logarithms of algebraic numbers and the reduction procedure involving the theory of continued fractions, to explicitly ...
Herbert Batte +2 more
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Padovan and Perrin numbers of the form 7ᵗ-5ᶻ-3ʸ-2ˣ [PDF]
Notes on Number Theory and Discrete MathematicsConsider the Padovan sequence (pₙ)ₙ≥₀ given by pₙ₊₃=pₙ₊₁+pₙ with p₀=p₁=p₂=1. Its companion sequence, the Perrin sequence (℘ₙ)ₙ≥₀, follows the same recursive formula as the Padovan numbers, but with different initial values: p₀=3, p₁=0 and p₂=2.
Djamel Bellaouar +2 more
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Padovan and Perrin Numbers as Sums of Two Jacobsthal Numbers
, 2022 Let $\left\lbrace P_{k}\right\rbrace_{k\geq0}$ be the Padovan sequence defined by $P_{k}=P_{k-2}+P_{k-3}$ with initial values are $P_{0}=P_{1}=P_{2}=1$. Let $\left\lbrace R_{k}\right\rbrace_{k\geq0}$ be the Perrin sequence defined by $R_{k}=R_{k-2}+R_{k-3}$ with initial values are $R_{0}=3$, $R_{1}=0$, $R_{2}=2$.
Ismail, Mustafa, Gaber, Ahmed, Anwar, M.
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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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