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Padovan and Perrin numbers as product of two repdigits
Boletin De La Sociedad Matematica Mexicana, 2022Let \((P_n)_{n\ge 0}\) and \((E_n)_{n\ge 0}\) be the sequences of \textit{Padovan numbers} and \textit{Perrin numbers}, respectively, defined by the linear recurrences: \begin{align*} P_0=P_1=P_2=1 \quad \text{and} \quad & P_{n+3}=P_{n+1}+P_n\quad \text{for all} \quad n\ge 0, \quad \text{and}\\ E_0=2, ~ E_1=0, ~ E_2=2 \quad \text{and} \quad & E_{n+3 ...
Salah Eddine Rihane +2 more
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Multiplicative dependence between Padovan and Perrin numbers
Boletin De La Sociedad Matematica Mexicana, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Behera, Mitashree, Ray, Prasanta Kumar
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Padovan and Perrin Numbers Which are Products of Two Repdigits in Base b
Results in Mathematics, 2021In this paper, we find all Padovan and Perrin numbers which can be expressible as a products of two repdigits in the base b with 2 ≤ b ≤ 10. It is shown that the largest Padovan and Perrin numbers which can be expressible as a products of two repdigits are P_25 = 616 and T_22 = 486, respectively.
Kouessi Norbert Adedji +2 more
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On b-concatenations of Padovan and Perrin numbers
Boletin De La Sociedad Matematica MexicanazbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kouessi Norbert Adedji +2 more
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On Fibonacci–Hessenberg matrices and the Pell and Perrin numbers
Applied Mathematics and Computation, 2012The author gives examples of recursive sequences of Hessenberg matrices \(A_{n}\) (\(n=1,2,\dots\) where \(A_{n}\) is \(n\times n\)) for which the sequences \(\left\{ \det A_{n}\right\} \) satisfy a simple second order recurrence relation. Proofs are elementary.
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Social Distancing, Primes, and Perrin Numbers
Math Horizons, 2021Harry Dweighter is a longtime restaurant owner who is famous for pondering the mathematics behind flipping pancakes (Problem E2569, Amer. Math. Monthly, 82 [1975], 1010).
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Perrin numbers expressible as sums of two base b repdigits
2021Let \( (P_n)_{n\ge 0} \) be the sequence of \textit{Perrin numbers} defined by the ternary recurrence relation \( P_{n+3}=P_{n+1}+P_n \), with the initial conditions \( P_0=3 \), \( P_1=0 \), and \( P_2=2 \). For an integer \( b\ge 2 \), a natural number \( N \) od the form \( N=a\left(\dfrac{b^{\ell}-1}{b-1}\right) \) for some \( \ell\ge 2 \) and \( a\
Bhoi, Khisan, Ray, Prasanta Kumar
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On perfect powers that are difference of two Perrin numbers or two Padovan numbers
Proceedings of the Indian National Science AcademyMerve Guney Duman
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Perrin Numbers Which Are the Sum, Difference, or Product of Two Fibonacci Numbers
The Fibonacci QuarterlyZ Boughadi, Abdelaziz El Habibi
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Padovan or Perrin numbers that are concatenations of two distinct base b repdigits
Mathematica Slovaca, 2023Abstract Let {P n } n⩾0 be the Padovan sequence with initial conditions P 0=0, P 1=1, and P 2=1 and the recurrence relation P n+3=P
Adédji, Kouèssi N. +3 more
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