Faculty Publication: Professor Emeritus of Mathematics Helen G. Grundman

A Note on Gaps Between Happy Numbers

Authors: Helen G. Grundman

Source: Rocky Mountain Journal of Mathematics, Volume: 54, Issue: 2, Pages: 491-494, DOI: 10.1216/rmj.2024.54.491, April 2024

Type of Publication: Article

Abstract: Fix a base b≥2 and an exponent e≥2. An 𝑒-power 𝑏-happy number is a positive integer that reaches 1 under iteration of the function mapping a positive integer to the sum of the 𝑒-th powers of its base 𝑏 digits. In this note, we answer the question of how large the gaps between 𝑒-power 𝑏-happy numbers can be.

Mathematics