On Hardy's Apology Numbers

TL;DR

This paper generalizes and classifies twelve well-known recreational numbers into three types, introducing a novel proof method and combinatorial operators to facilitate their systematic search and analysis.

Contribution

It presents a new classification scheme for recreational numbers and introduces innovative proof techniques and combinatorial operators for their systematic identification.

Findings

Successful classification of twelve recreational numbers into three types.

Development of a novel proof method for limiting the search space.

Introduction of combinatorial operators to aid programming and search processes.

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.