再论 Collatz 猜想及检测特殊子序列上循环的闭式 [断言：Collatz 循环]
离散数学
2011-08-23 v1
摘要
西印度群岛大学的 Cadogan 教授识别出了能产生归一化常数 k 始终为 1 的长子序列的特殊起始点。我研究了这些特殊序列，并发现了一个隐式的混合整数闭式方程，若对其求解，将能产生循环子序列中的种子值。此类循环仅出现在极大数之间，导致该方程难以进行数值求解。
引用
@article{arxiv.1108.4056,
title = {More Jabber about the Collatz Conjecture and a Closed Form for Detecting Cycles on Special Subsequences [Assertion: Collatz cycles]},
author = {Thomas W. Lynch},
journal= {arXiv preprint arXiv:1108.4056},
year = {2011}
}
备注
Write me if you would like a copy of the Mathematica program I used to search against the constraint. There are some variations for the closed form on other cases, write if you would like those. This work was done while I was visiting at the University of the West Indies this summer. I truly enjoyed meeting Dr. Cadogan and studying his Collatz conjecture proofs