Hankel determinants of the Cantor sequence

Zhi-xiong Wen, Wen Wu

Published 2014-07-14, updated 2014-10-24Version 2

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.