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Hankel determinants of the Cantor sequence

In the paper, we give the recurrent equations of the Hankel determinants of the Cantor sequence, and show that the Hankel determinants as a double sequence is 3-automatic. With the help of the Hankel determinants, we prove that the irrationality exponent of the Cantor number, i.e. the transcendental number with Cantor sequence as its b-ary expansion, equals 2.

preprint2014arXivOpen access
Zhi-xiong WenWen Wu
math.COmath.NT
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Zhi-xiong WenWen Wu

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