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arXiv · 1310.2138

On the irrationality exponent of the regular paperfolding numbers

Yingjun Guo·Wen Wu·Zhixiong Wen
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Abstract

In this paper, improving the method of Allouche \emph{et al.} \cite{APWW98}, we calculate the Hankel determinant of the regular paperfolding sequence, and prove that the Hankel determinant sequence module 2 is periodic with period 10 which answers Coon's conjecture \cite{CV12}. Then we extend Bugeaud's method \cite{Bugeaud11} to obatin the exact value of the irrationality exponent for some general transcendental numbers. Using the results above, we prove that the irrationality exponents of the regular paperfolding numbers are exactly 2.

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BibTeXRIS

Yingjun Guo, Wen Wu, Zhixiong Wen. 2013-10-08. On the irrationality exponent of the regular paperfolding numbers. https://doi.org/10.1016/j.laa.2013.12.023

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