For a base \(b \ge 2\) , the b-elated function, \(E_{2,b}\) , 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 \(E_{2,b}\) . 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 \(E_{2,b}\) 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.
