关于Mersenne数列的进一步探讨  

Further Explore on Mersenne Sequences

作　　者：姜莲霞 JIANG Lian-xia(School of Mathematics and Statistics,Kashi University,Kashi 844008,Xinjing,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844008

出　　处：《喀什大学学报》2018年第3期6-10,共5页Journal of Kashi University

基　　金：新疆维吾尔自治区自然科学基金资助项目(2017D01A13)

摘　　要：由Mersenne数列的通项公式得到了该数列的一些性质.基于此,首先研究了Jacobsthal数列和Jacobsthal-Lucas数列,目的是揭示它们与Mersenne数之间的关系;其次讨论了这些数列前n项和的计算,以及项之和与积的问题;最后给出了Mersenne数列的生成矩阵、三对角矩阵和g-循环矩阵的一些重要结果.Some properties were obtained by the general formula of the Mersenne sequence.Based on this,first,in order to show the relationship between Jacobsthal numbers or Jacobsthal-Lucas numbers and Mersenne numbers,we study the Jacobsthal sequence and Jacobsthal-Lucas sequence.Secondly,we discuss the calculation of the sum of the first n terms in these sequences,and the sum and the product of its items.Finally,some important results of generation matrix,tridiagonal matrix and g-circulation matrix of Mersenne sequence are given.

关 键 词：MERSENNE数 Jacobsthal数 Jacobsthal-Lucas数 G-循环矩阵 

分 类 号：O151.21[理学—数学]