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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Abstract 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.
AbstractList 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.
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.
Author da Silva, R.
de Oliveira, K. S.
da Graça Neto, A. C.
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Issue 4
Keywords generalized Fibonacci number
Jacobsthal numbers
Padovan numbers
arithmetic properties
Narayana numbers
Pell numbers
Language English
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Snippet In this paper, we study arithmetic properties of the recently introduced sequence , for some values of its parameters. These new numbers simultaneously...
In this paper, we study arithmetic properties of the recently introduced sequence , for some values of its parameters. These new numbers simultaneously...
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639/766/189
639/766/530
639/766/747
Algebra
Arithmetic
Factorials
Fibonacci numbers
Mathematics
Mathematics and Statistics
Parameters
Sequences
Title An Arithmetic Approach to a Four-Parameter Generalization of Some Special Sequences
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