English

On Hardy's Apology Numbers

Number Theory 2022-03-30 v1

Abstract

Twelve well known `Recreational' numbers are generalized and classified in three generalized types Hardy, Dudeney, and Wells. A novel proof method to limit the search for the numbers is exemplified for each of the types. Combinatorial operators are defined to ease programming the search.

Cite

@article{arxiv.2008.08187,
  title  = {On Hardy's Apology Numbers},
  author = {Henk Koppelaar and Peyman Nasehpour},
  journal= {arXiv preprint arXiv:2008.08187},
  year   = {2022}
}
R2 v1 2026-06-23T17:57:04.350Z