| Autor: |
Clokie, Trevor, Lidbetter, Thomas F., Molina Lovett, Antonio J., Shallit, Jeffrey, Witzman, Leon |
| Jazyk: |
angličtina |
| Rok vydání: |
2020 |
| Předmět: |
|
| DOI: |
10.4230/lipics.fun.2021.10 |
| Popis: |
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. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
|
