SOME REMARKS ABOUT THE COLLATZ PROBLEM

被引：0

作者：

Rystsov, I. K. ^{[1
]}

机构：

[1] Natl Tech Univ Ukraine, Kyiv Polytech Inst, Kiev, Ukraine

来源：

CYBERNETICS AND SYSTEMS ANALYSIS | 2013年 / 49卷 / 03期

关键词：

(3x + 1)problem; Collatz conjecture; affine automaton;

D O I：

10.1007/s10559-013-9518-z

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper considers the Collatz conjecture (the 3x+ 1 problem). A new form of the Collatz function is proposed that can be analytically studied. The structure of the kernel of this function is analyzed by affine automata and is used to construct an increasing hierarchy of Bohm-Sontacchi numbers. Successful trajectories of Collatz function iterations are coded by natural numbers and any natural number is shown to be a code of some trajectory.

引用

页码：353 / 365

页数：13

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