论文标题
Collatz序列的奇偶元向量的特征数字和特征方程
Characteristic numbers and characteristic equations of parity vectors of Collatz sequences
论文作者
论文摘要
目前的工作涉及Collatz序列（有限和无限长度）的奇偶元向量的表征。这样的表征会导致确定几个数字（整数或非智能者），我们称为给定平价向量的特征数。某些特征数是通过方程式链接在一起的，这些方程式可以称为所考虑的平价向量的特征方程。如果有限长度n的奇偶元向量v包含无限长度的奇偶元向量v的前n个术语，则V的所有特征数被视为无限矢量V的特征n的特征数。当N倾向于无限属性构成无限量的无限属性构成Infinite Vector Vector v和它们允许其行为和属性确定行为和属性。在本文中，我们根据其特征数量研究了无限长度的奇偶校验矢量的特性。然后，我们建立了Collatz序列的第一项与其平价向量之间的关系。最后，仍然基于特征数字，我们确定存在分歧序列的某些存在条件和不存在的条件。
The present work deals with the characterization of parity vectors of Collatz sequences (of finite and infinite length). Such a characterization leads to the determination of several numbers (integers or non-integers) that we call the characteristic numbers of a given parity vector. Some characteristic numbers are linked together by equations that can be called characteristic equations of the considered parity vector. If a parity vector v of finite length n contains the first n terms of a parity vector V of infinite length then all the characteristic numbers of v are considered as characteristic numbers of order n of the infinite vector V. The limits of nth order characteristic numbers when n tends to infinity constitute the absolute characteristic numbers of the infinite vector V and they allow determining its behavior and properties. In this paper, we study the properties of parity vectors of infinite length based on their characteristic numbers. Then, we establish the relations between the first term of a Collatz sequence and its parity vector. Finally, still based on the characteristic numbers, we determine some conditions of existence and non-existence of divergent sequences.
