FIBONACCI SEQUENCE AND CANTOR'S TERNARY SET

ＩＢＯＮＡＣＣＩＳＥＱＵＥＮＣＥＡＮＤＣＡＮＴＯＲ′ＳＴＥＲＮＡＲＹＳＥＴＴＯＮＧＪＩＮＧＣＨＥＮＧＳＡＭＯＮＳ，Ｊ．ＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＳｅｐｔｅｍｂｅｒ１２，１９９４．ＲｅｖｉｓｅｄＤｅｃｅｍｂｅｒ１５，１９９６．Ｄｅｐａｒ...     

一类递归序列通项的近似计算

研究广义费波那契序列通项公式的计算方法．利用整系数多项式正根理论,得到了广义费波那契序列通项的一个十分精确的近似计算方法．     

The game of n-times nim

The following game is considered. The first player can take any number of stones, but not all the stones, from a single pile of stones. After that, each player can take at most n-times as many as the previous one. The player first unable to move loses and his opponent wins. Let f₁,f₂,… be an initial sequence of stones in increasing order, such that the second player has a winning strategy when play begins from a pile of size f_i. It is proved that there exist constants c=c(n) and k₀=k₀(n) such that f_k+1=f_k+f_k−c for all k>k₀, and lim_n→∞ c(n)/(nlogn)=1.     

小麦植株节间长度分析

在小麦高产育种中,除根据产量及其构成因素进行选育外,对与产量有关的植株形态性状及生理特性进行选择也是育种者要考虑的问题.多年来,对于株高性状的选育引起了普遍重视,并且小麦植株高度的差异主要决定于各节间长度的差异,对此有关专家作了大量研究.通过对斐波那契数列的研究,提出了广义斐波那契数列出概念并用统计分析的方法对采集的小麦茎秆的数据进行数据分析,得到了小麦的茎秆结构符合广义斐波那契数列的结论.研究为简化小麦茎秆研究提出了数学上的理论支持.     

Fibonacci数列的模数列的周期性

对于Fibonacci数列{Fn}以及给定的正整数m,由Fn关于模m的最小非负剩余an,构成一个新的数列{an},称为Fibonacci数列的模数列.本文利用初等数论的知识和数学归纳法,证明了Fibonacci数列的模数列是周期数列,并且是纯周期数列.     

Wythoff''s sequence and -Heap Wythoff''s conjectures

Define a Wythoff's sequence as a sequence of pairs of integers (A_n,B_n) _n>n0 such that there exists a finite set of integers T, A_n=mex( A_i,B_i:i<n T), B_n-A_n=n, and B_n ∩T=. Structural properties and behaviors of Wythoff's sequence are investigated. The main result is that for such a sequence, there always exists an integer α such that when n is large enough, |A_n-nφ-α|1, where , the golden section. The value of α can also be easily determined by a relatively small number of pairs in the sequence. As a corollary, the two conjectures on the N-heap Wythoff's game by Fraenkel [Complexity, appeal and challenges of combinatorial Games, Theoret. Comput. Sci. 313 (2004) 393–415] on the N-heaped Wythoff's game are proved to be equivalent.     

广义的k阶Fibonacci-Jacobsthal序列及其性质

定义了一类广义的k阶Fibonacci-Jacobsthal序列,并给出了第四个初值条件.借助矩阵的方法得到了Jacobsthal序列与Jacobsthal-Lucas序列的关系,广义k阶Fibonacci-Jacobsthal序列与Jacobsthal序列,Fibonacci序列的关系,同时给出了k阶Fibonacc...     

On the Lucas Base and Computation of Counting Function Mean Value

In this paper, we introduce a new counting function a(m) related to the Lucas number, then use conjecture and induction methods to give an exact formula Ar(N)=α(n), (r=1,2,3) and prove them.