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On some conjectures of P. Barry
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-04-26 , DOI: 10.1016/j.jnt.2021.03.015
J.-P. Allouche , G.-N. Han , J. Shallit

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 q2, 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.



中文翻译:

关于巴里(P. Barry)的一些猜想

我们证明了P. Barry最近提出的许多猜想,它们与折纸序列和Rueppel序列有关。此外,我们研究了本文涉及的序列的规律性,并证明了对于所有q2个,由正整数组成的序列,其奇数部分的形式为 4ķ+1个不是q-常规的。最后,我们建立了两个汉克行列式序列的2正则性。

更新日期:2021-04-27
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