Cycles of higher-order Collatz sequences

被引：0

作者：

Simons, John L. ^{[1
]}

机构：

[1] Univ Groningen, POB 800, NL-9700 AV Groningen, Netherlands

来源：

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | 2022年 / 28卷 / 01期

关键词：

Collatz problem; Higher order difference equation; Linear form in logarithms; RATIONAL LINEAR FORM; LOGARITHMS;

D O I：

10.7546/nntdm.2022.28.1.48-63

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider a sequence of numbers x(n) is an element of Z(+) defined by x(n+1) = x(n)/2 if x(n) is even, and x(n+1) = x(n) + 2x(n-1) + q/2 if xn is odd. A 1-cycle is a periodic sequence with one transition from odd to even numbers. We prove theoretical and computational results for the existence of 1-cycles, and discuss a generalization to more complex cycles.

引用

页码：48 / 63

页数：16

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