On some conjectures of P. Barry

[摘要] We prove a number of conjectures recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence. Furthermore, we study the regularity of sequences involved in the paper, and prove that for all q >= 2, the sequence consisting of the positive integers whose odd part is of the form 4k + 1 is not q-regular. Finally we establish the 2-regularity of two sequences of Hankel determinants. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-01

[关键词] Hankel determinant;Rueppel sequence;Paperfolding sequence;Automatic sequence;Regular sequence