关于某些Collatz轨线的第一合并点的分布
On the Distribution of the First Point of Coalescence for some Collatz Trajectories
摘要：
本文对Collatz函数的某些轨迹进行了数值计算。具体来说，我通过一个复杂的算法来评估每个整数$n\equiv 0 (\bmod{2})$和$n\equiv 2(\bmod{3})$的聚结点，该算法已经被开发用于测试任何不同的模数类。发现的数据表明，第一个聚并点的分布与某些指数型丢番图方程的解密切相关。然后，我证明了整数$n$和$3n+2$的第一个合并点似乎倾向于期望值$4/5n$。当算法被推到其峰值估计时，已经发现期望值开始偏离$4/5n$的初始估计。第一点的合并的整数$n$和$3n+2$出现根除从“一步一步”的观点，但从拓扑的角度来看，似乎是本地化的丢番图解决方案的一些特定的功能。
英文摘要：
This paper is a numerical evaluation of some trajectories of the Collatz function. Specifically, I assess the coalescence points of each integer $n\equiv 0 (\bmod{2})$ and $n\equiv 2(\bmod{3})$ through a sophisticated algorithm that has been developed to test on any different modulus classes. The data discovered illustrate that the distribution of the first point of coalescence is closely related to the solutions of some exponential diophantine equation. Afterwards, I show that the first point of coalescence of the integers $n$ and $3n+2$ appear to tend to an expected value of $4/5n$. When the algorithm was pushed to its peak estimation it has been discovered that the expected value begins to deviate from the initial estimation of $4/5n$. The first point of coalescence of the integers $n$ and $3n+2$ appear eradicate from a "step by step" point of view but from a topological point of view seem to be localized around the diophantine solution of some particular functions.
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