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Cloitre's Self-Generating Sequence (2501.00784v1)
Published 1 Jan 2025 in math.CO, cs.DM, cs.FL, and math.NT
Abstract: In 2009 Benoit Cloitre introduced a certain self-generating sequence $$(a_n){n\geq 1} = 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, \ldots,$$ with the property that the sum of the terms appearing in the $n$'th run equals twice the $n$'th term of the sequence. We give a connection between this sequence and the paperfolding sequence, and then prove Cloitre's conjecture about the density of $1$'s appearing in $(a_n){n \geq 1}$.