论文标题
步行到斐波那契序列上的无穷大
Walking to Infinity on the Fibonacci Sequence
论文作者
论文摘要
数字理论中一个有趣的开放问题询问是否可以在素数上步行到无穷大，在该序列中的每个术语都比以前的数字多。在本文中，我们研究了它在斐波那契序列上行走的变化。我们证明，所有步行都以斐波那契数开头，以下术语是斐波那契数的数字，该数字是通过一次右边的一个数字附加到右边的一个数字获得的最多长度为两个。在更普遍的情况下，我们每次最多都有数量数字的数量，我们为最长步行的长度提供一个公式。
An interesting open problem in number theory asks whether it is possible to walk to infinity on primes, where each term in the sequence has one more digit than the previous. In this paper, we study its variation where we walk on the Fibonacci sequence. We prove that all walks starting with a Fibonacci number and the following terms are Fibonacci numbers obtained by appending exactly one digit at a time to the right have a length of at most two. In the more general case where we append at most a bounded number of digits each time, we give a formula for the length of the longest walk.
