Sequences of consecutive factoradic happy numbers

Joshua Carlson, Eva G. Goedhart, Pamela E. Harris

Given a positive integer $n$, the factorial base representation of $n$ is given by $n={\sum }_{i=1}^k{a}_i\cdot i!$, where $a_k\ne 0$ and $0\le a_i\le i$ for all $1\le i\le k$. For…