An Arithmetic Approach to a Four-Parameter Generalization of Some Special Sequences

In this paper, we study arithmetic properties of the recently introduced sequence , for some values of its parameters. These new numbers simultaneously generalizes a number of well-known sequences, including the Fibonacci, Pell, Jacobsthal, Padovan, and Narayana numbers. We generalize a recent arith...

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Published inP-adic numbers, ultrametric analysis, and applications Vol. 12; no. 4; pp. 322 - 332
Main Authors da Silva, R., da Graça Neto, A. C., de Oliveira, K. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.10.2020
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Algebra
Arithmetic
Factorials
Fibonacci numbers
Mathematics
Mathematics and Statistics
Parameters
Sequences
generalized Fibonacci number
Jacobsthal numbers
Padovan numbers
arithmetic properties
Narayana numbers
Pell numbers
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Summary:In this paper, we study arithmetic properties of the recently introduced sequence , for some values of its parameters. These new numbers simultaneously generalizes a number of well-known sequences, including the Fibonacci, Pell, Jacobsthal, Padovan, and Narayana numbers. We generalize a recent arithmetic property of the Fibonacci numbers to . In addition, we also study the -adic order and find factorials in this sequence for certain choices of the parameters. All the proof techniques required to prove our results are elementary.
ISSN:2070-0466
2070-0474
DOI:10.1134/S2070046620040068