Sequences of Consecutive Happy Numbers in Negative Bases

Helen G. Grundman, Pamela E. Harris

For $b\le -2$ and $e\ge 2$, let $S_{e,b}:\mathbb{Z}\to {\mathbb{Z}}_{\ge 0}$ be the function taking an integer to the sum of the $e$-powers of the digits of its base $b$ expansion…