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

被引：0
|
作者：
da Silva, R. [1 ]
da Graca Neto, A. C. [2 ]
de Oliveira, K. S. [3 ]
机构：
[1] Univ Fed Sao Paulo, BR-12247014 Sao Jose Dos Campos, SP, Brazil
[2] Univ Estado Amazonas, BR-69055038 Manaus, AM, Brazil
[3] Univ Fed Amazonas, BR-69103128 Manaus, AM, Brazil
来源：
P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS | 2020年 / 12卷 / 04期
关键词：
generalized Fibonacci number; Pell numbers; Padovan numbers; Jacobsthal numbers; Narayana numbers; arithmetic properties; FIBONACCI; ORDER;
D O I：
10.1134/S2070046620040068
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study arithmetic properties of the recently introduced sequence F(r,s)i(k, n), 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 F-r,s(1)(2, n). In addition, we also study the 2-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.
引用
收藏
页码：322 / 332
页数：11
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