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A pair of rational double sequences. (English) Zbl 1497.40006

Summary: Double sequences appear in a natural way in cases of iteratively given sequences if the iteration allows to determine besides the successors from the predecessors also the predecessors from their followers. A particular pair of double sequences is considered which appears in a parqueting-reflection process of the complex plane. While one end of each sequence is a natural number sequence, the other consists of rational numbers. The natural numbers sequences are not yet listed in OEIS Wiki. Complex versions from the double sequences are provided.

MSC:

40A99 Convergence and divergence of infinite limiting processes

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References:

[1] S. A. Abdymanapov, S. Altynbek, A. Begehr and H. Begehr, 1, 2, 3, some inductive real sequence and a beautiful algebraic pattern, Analysis (2021), 10.1515/anly-2020-0014. · Zbl 1484.39008 · doi:10.1515/anly-2020-0014
[2] H. Begehr, H. Lin, H. Liu and B. Shupeyeva, An iterative real sequence based on \sqrt{2} and \sqrt{3} providing a plane parqueting and harmonic Green functions, Complex Var. Elliptic Equ. 66 (2021), no. 6-7, 988-1013. · Zbl 1469.30087
[3] N. G. A. Sloane, The on-line encyclopedia of integers sequences, The OEIS Foundation Inc, http://oeis.org, 2018.
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