2026-07-24T05:42:05Z https://drops.dagstuhl.de/oai

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Computational Fun with Sturdy and Flimsy Numbers Clokie, Trevor Lidbetter, Thomas F. Molina Lovett, Antonio J. Shallit, Jeffrey Witzman, Leon sturdy number flimsy number context-free grammar finite automaton enumeration 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Trevor Clokie and Thomas F. Lidbetter and Antonio J. Molina Lovett and Jeffrey Shallit and Leon Witzman 2020 Is Part Of LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FUN.2021.10 urn:nbn:de:0030-drops-127715 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.10 eng https://creativecommons.org/licenses/by/3.0/legalcode