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Elated Numbers
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DOI：10.1007/s44007-025-00185-7.png)
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Abstract
En 中文
For a base b >= 2, the b-elated function, E-2,E-b, maps a positive integer written in base b to the product of its leading digit and the sum of the squares of its digits. A b-elated number is a positive integer that maps to 1 under iteration of E-2,E-b. The height of a b-elated number is the number of iterations required to map it to 1. We determine the fixed points and cycles of E-2,E-b and prove a range of results concerning sequences of b-elated numbers and b-elated numbers of minimal heights. Although the b-elated function is closely related to the b-happy function, the behaviors of the two are notably different, as demonstrated by the results in this work.
Keywords:
Digital problems
Integer sequences
Elated numbers
Happy numbers
Cycles
Heights
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