Demonstrates new insights into Lucas's work on the Tower of Hanoi and Frame-Stewart conjecture, revealing connections with Lucas sequences.
On the occasion of the 150th baptism anniversary of the Fibonacci sequence we evoke some other achievements of the French mathematician François Édouard Anatole Lucas. His Tower of Hanoi with three pegs, for whose recursive solution we present a new minimality proof, led to the still challenging Frame-Stewart conjecture for larger numbers of pegs. We show that two elementary Lucas sequences are subsequences of Frame-Stewart numbers. For the special case of four pegs we employ the product logarithm to specify the corresponding subsequence.
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Hinz et al. (2026) studied this question.
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