论文标题
结实和脆弱数字的计算方面
Computational Aspects of Sturdy and Flimsy Numbers
论文作者
论文摘要
在斯托拉斯基之后，我们说，如果n的某些正倍在基本B中的数字总和比n的数字较小，则在基本B中是脆弱的。否则它是坚固的。我们开发了用于研究结实和脆弱数量的算法方法。 我们提供了一些确定数字是否坚固的标准。为了关注基本B = 2的情况，我们研究了检查给定数字是否坚固的计算问题，为该问题提供了多种算法。我们发现另外两个以前未知的坚固素数。我们开发了一种确定二进制中固定数为0的数字的方法。最后，我们开发了一种方法，使我们能够估计具有n位的k-峰数量的数量，并为k = 3和k = 5提供明确的结果。我们的结果证明了基于自动机理论的方法，证明了创建数量理论问题算法的实用性（和有趣）。
Following Stolarsky, we say that a natural number n is flimsy in base b if some positive multiple of n has smaller digit sum in base b than n does; otherwise it is sturdy. We develop algorithmic methods for the study of sturdy and flimsy numbers. We provide some criteria for determining whether a number is sturdy. Focusing on the case of base b = 2, we study the computational problem of checking whether a given number is sturdy, giving several algorithms for the problem. We find two additional, previously unknown sturdy primes. We develop a method for determining which numbers with a fixed number of 0's in binary are flimsy. Finally, we develop a method that allows us to estimate the number of k-flimsy numbers with n bits, and we provide explicit results for k = 3 and k = 5. Our results demonstrate the utility (and fun) of creating algorithms for number theory problems, based on methods of automata theory.
