在斐波那契数列上走向无穷大
Walking to Infinity on the Fibonacci Sequence
摘要：
数论中一个有趣的开放问题是，是否有可能在素数上走到无穷大，其中序列中的每一项都比前一项多一位。在本文中，我们研究它的变化，我们走在斐波那契序列。我们证明了，所有的行走开始于一个斐波那契数和以下条款是斐波那契数通过追加一个数字在一个时间的权利有一个长度最多为2。在更一般的情况下，我们每次最多附加一个有界的数字，我们给出了最长行走长度的公式。
英文摘要：
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.
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