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Padovan numbers that are concatenations of a Padovan number and a Perrin number

Periodica Mathematica Hungarica
The 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
Merve Guney Duman
exaly   +5 more sources

New Types of Distance Padovan Sequences via Decomposition Technique

Applied Sciences (Switzerland), 2022
In this paper, we introduce new kinds of generalized Padovan sequences and study their properties using number decomposition techniques. In particular, we consider three types of generalized Padovan sequences defined by the same recurrence equation with ...
Małgorzata Wołowiec-Musiał, Bednarz Urszula, Andrzej Włoch   +2 more
exaly   +4 more sources

Generalized Padovan Numbers

Symmetry
In this paper, we study a generalization of Padovan numbers. We define a generating function and matrix generators for the generalized Padovan sequence. Moreover, using graph methods and a special family of generalized Padovan sequences, we derive a multinomial formula for generalized Padovan numbers. We also prove some identities that generalize known
Małgorzata Wołowiec-Musiał, Andrzej Włoch   +1 more
exaly   +3 more sources

Padovan and Perrin Hybrid Number Identities

Communications in Advanced Mathematical Sciences, 2021
This work investigates the numbers of Padovan and Perrin hybrids. At first, the hybrid numbers, the sequences in the hybrid form, and their matrix forms are ordered as studied sequences. Thus, it was possible to display the negative index hybrids, define
Renata Vieira, Milena Mangueira, Francisco Regis Alves, Paula Maria Machado Cruz Catarino   +3 more
doaj   +3 more sources

On Gaussian Jacobsthal-Padovan Numbers

Cumhuriyet Science Journal, 2022
Gaussian Jacobsthal-Padovan numbers have been the central focus of this paper and firstly this number sequence has defined. Later, we have given the proof of the generating function of the Gaussian Jacobsthal-Padovan sequence.
Nusret Karaaslan
doaj   +3 more sources

The Hybrid Numbers of Padovan and Some Identities

Annales Mathematicae Silesianae, 2020
In this article, we will define Padovan’s hybrid numbers, based on the new noncommutative numbering system studied by Özdemir ([7]). Such a system that is a set involving complex, hyperbolic and dual numbers.
Mangueira Milena Carolina dos Santos, Vieira Renata Passos Machado, Alves Francisco Régis Vieira, Catarino Paula Maria Machado Cruz   +3 more
doaj   +2 more sources

Repdigits as sums of three Padovan numbers [PDF]

Boletin De La Sociedad Matematica Mexicana, 2019
AbstractLet $$ \{P_{n}\}_{n\ge 0} $${Pn}n≥0 be the sequence of Padovan numbers defined by $$ P_0=0 $$P0=0, $$ P_1 =1=P_2$$P1=1=P2, and $$ P_{n+3}= P_{n+1} +P_n$$Pn+3=Pn+1+Pn for all $$ n\ge 0 $$n≥0. In this paper, we find all repdigits in base 10 which can be written as a sum of three Padovan numbers.
Mahadi Ddamulira
exaly   +7 more sources

Some New Graph Interpretations of Padovan Numbers

Symmetry
Padovan numbers and Perrin numbers belong to the family of numbers of the Fibonacci type and they are well described in the literature. In this paper, by studying independent (1,2)-dominating sets in paths and cycles, we obtain new binomial formulas for Padovan and Perrin numbers.
Iwona Włoch, Andrzej Włoch, Mateusz Pirga   +2 more
exaly   +2 more sources

The Extension of Added Sugar Use in Packaged Foods Targeted at Children in Brazil. [PDF]

Matern Child Nutr
ABSTRACT Excessive added sugars intake in early childhood has been associated with an increased risk of obesity and other non‐communicable diseases. In Brazil, packaged foods form a substantial part of children's diets, yet no studies have examined the presence of added sugars in products specifically marketed to this population.
Valls M, Scapin T, Padovan M, Kraemer MVDS, Fernandes AC, Bernardo GL, Uggioni PL, Chaddad MCC, Proença RPC.   +8 more
europepmc   +2 more sources

Some geometric properties of the Padovan vectors in Euclidean 3-space [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
Padovan numbers were defined by Stewart (1996) in honor of the modern architect Richard Padovan (1935) and were first discovered in 1924 by Gerard Cordonnier.
Serdar Korkmaz, Hatice Kuşak Samancı
doaj   +1 more source