On some conjectures of P. Barry
J.-P. Allouche, G.-N. Han, J. Shallit

TL;DR
This paper proves several conjectures related to the paperfolding and Rueppel sequences, advancing understanding in sequence theory and confirming prior hypotheses.
Contribution
It provides proofs for multiple conjectures concerning the properties of the paperfolding and Rueppel sequences, clarifying their structure and behavior.
Findings
Confirmed conjectures about the paperfolding sequence
Validated properties of the Rueppel sequence
Enhanced theoretical understanding of these sequences
Abstract
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.
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