Mathematical proof demonstrates finite limits for digit-appending walks along Fibonacci sequences across integer bases, indicating that infinite walks are impossible under bounded digit additions.
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≥ 2 when at most N digits are appended per step. Our proof method is base-independent, yielding the bound \[L \;≤\; 2Nlog_φb \,+\, O(1),\] uniformly in the starting term, without relying on base-specific periodicity computations (here, φ=1+√52). Our approach extends to certain Lucas sequences.
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