文章基本信息

标题：Computational Fun with Sturdy and Flimsy Numbers
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作者：Trevor Clokie ; Thomas F. Lidbetter ; Antonio J. Molina Lovett 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：157
页码：10:1-10:21
DOI：10.4230/LIPIcs.FUN.2021.10
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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 0âs 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.
关键词：sturdy number; flimsy number; context-free grammar; finite automaton; enumeration