Self-Referential Leading Digits of Exponential Sequences: Arithmetic Structure and Certified Search

Zihang Fang

For $c>1$ and an integer radix $b\ge 2$, we study the positive integers $m$ for which $m{b}^k\le c^m<(m+1)b^k$ for some $k\ge 0$; for integer $c$, this is the self-prefix leading-digit…