3n+1问题：利益分割
The 3n+1 problem: a partition of interest
摘要：
与Collatz映射共轭的映射似乎意味着$\N=\{1,2,3,\ldots\}$被划分为平凡循环$\{1\}$和“字符串”，“字符串”是从$\{2+3\0\}$的元素到$\{3+4\0\}$的元素的$\{\N \setminus 1\}$的有序子集（$\0=0 \cup \N$）。特别地，这意味着除了平凡循环之外的所有轨迹都经过$\{3+4\0\}$的元素（原始映射的$\{5+8\0\}$）。我给这个猜想的理由。接下来，我注意到3n+1和3n+3是广义$3n+p, p \in \{\ldots,-3,-1,1,3,\ldots\}$中似乎存在这种划分的唯一数。令人怀疑的是，这些也是唯一的成员的猜想（减少到平凡的循环）似乎举行。
英文摘要：
A mapping conjugate to the Collatz mapping seems to imply that $\N=\{1,2,3,\ldots\}$ is partitioned in a trivial loop $\{1\}$ and `strings' that are ordered subsets of $\{\N \setminus 1\}$ that run from an element of $\{2+3\0\}$ to an element of $\{3+4\0\}$ ($\0=0 \cup \N$). In particular, this means that all trajectories except for the trivial loop go through an element of $\{3+4\0\}$ ($\{5+8\0\}$ for the original mapping). I give reasons for this conjecture. Next, I note that the 3n+1 numbers and the 3n+3 numbers are the only numbers from the generalization $3n+p, p \in \{\ldots,-3,-1,1,3,\ldots\}$ for which such a partition seems to exist. Suspiciously, these are also the only members for which the conjecture (reduction to the trivial loop) seems to hold.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
