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Faculty Publication: Professor Emeritus of Mathematics Helen G. Grundman

June 14, 2024

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

Mathematics