论文标题
沿着某个数字理论序列步行到无穷大
Walking to Infinity Along Some Number Theory sequences
论文作者
论文摘要
一个有趣的开放猜想询问是否可以沿着素数步行到无穷大，在该序列中的每个术语都比上一个数字多。我们提出了用于Prime Walks的不同贪婪模型，以预测轨道轨迹的长时间行为，其中之一的行为与实际回溯类似。此外，我们研究了相同的猜想对无方数的数字，这是由于它们具有严格的正密度，而不是素数。我们介绍随机模型，并分析步行的预期长度和添加的数字频率。最后，我们证明不可能以其他重要的数字理论序列或不同基础的数字序列走到无限。
An interesting open conjecture asks whether it is possible to walk to infinity along primes, where each term in the sequence has one digit more than the previous. We present different greedy models for prime walks to predict the long-time behavior of the trajectories of orbits, one of which has similar behavior to the actual backtracking one. Furthermore, we study the same conjecture for square-free numbers, which is motivated by the fact that they have a strictly positive density, as opposed to primes. We introduce stochastic models and analyze the walks' expected length and frequency of digits added. Lastly, we prove that it is impossible to walk to infinity in other important number-theoretical sequences or on primes in different bases.
