论文标题
关于某些Collatz轨迹的第一点合并的分布
On the Distribution of the First Point of Coalescence for some Collatz Trajectories
论文作者
论文摘要
本文是对Collatz功能的某些轨迹的数值评估。具体来说，我通过复杂的算法通过复杂的算法来评估每个整数$ n \ equiv 0（\ bmod {2}）$和$ n \ equiv 2（\ bmod {3}）$的聚合点，这些算法已开发以测试任何不同的模量类别。发现的数据表明，合并的第一点的分布与某些指数二芬太汀方程的溶液密切相关。之后，我表明整数$ n $和3n+2 $的结合点似乎趋于预期价值$ 4/5n $。当将算法推向其峰值估计时，发现预期值开始偏离最初估计$ 4/5N $。整数$ n $和3n+2 $合并的第一点从“逐步”的角度消除了，但从拓扑角度来看，似乎围绕某些特定功能的Diophantine解决方案进行了定位。
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.
