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
收藏
页码：48 / 63
页数：16
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