Uniform Bounds for Digit-Appending Fibonacci Walks
Abstract
Building on the work of Miller et al. [Fibonacci Quarterly, 2022], we show that it is impossible to "walk to infinity" along the Fibonacci sequence in any integer base $b\geq 2$ when at most $N$ digits are appended per step. Our proof method is base-independent, yielding the bound \[L \;\leq\; 2N\log_φb \,+\, O(1),\] uniformly in the starting term, without relying on base-specific periodicity computations (here, $φ=\frac{1+\sqrt{5}}{2}$). Our approach extends to certain Lucas sequences.
Fields of Study & Subjects
Advanced Mathematical Theories and Applications
Advanced Combinatorial Mathematics
semigroups and automata theory
Publication details
- Journal / source
- The Fibonacci Quarterly
- Publisher
- Informa UK Limited
- Pages
- 1–10
- Publication date
- 3 September 2026
- Language
- EN