Collatz网络

摘要：

考虑到所有可能的路径，一个自然数可以采取以下Collatz猜想中提出的算法的规则，我们构建了一个图，可以被解释为一个无限的网络，考虑所有可能的路径内的猜想。这使我们能够理解为什么Collatz轨道的最小元素$x$等于1。随后，我们定义的扩展Collatz猜想等于$o x+1$时，$x$是奇数和$x/2$时，$x$是偶数与$o$一个奇数大于$3$，我们表明，有无限轨道的扩展Collatz猜想发散。最后，我们发现有趣的定理有关的斐波那契序列的素数。

英文摘要：

Considering all possible paths that a natural number can take following the rules of the algorithm proposed in the Collatz conjecture we construct a graph that can be interpreted as an infinite network that contemplates all possible paths within the conjecture. This allows us to understand why the minimal element of the Collatz orbit $x$ is equal to 1. Subsequently we define the extended Collatz conjecture equal to $o x+1$ when $x$ is odd and $x/2$ when $x$ is even with $o$ an odd number greater than $3$ and we show that there are infinite orbits in the extended Collatz conjecture that diverges. Finally, we find interesting theorems relating the Fibonacci sequence to prime numbers.

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。