Study on the non-periodicity of the generalized Thue-Morse sequences generated by cyclic permutations

Abstract

First we generalize the Thue-Morse sequence (the generalized Thue-Morse sequences) by a cyclic permutations and p-adic system, and consider the necessary-sufficient condition that it is non-periodic. Moreover if the generalized Thue-Morse sequence is not periodic, then all equally spaced subsequences of the generalized Thue-Morse sequences are not periodic. Finally we apply recently combinatorial transcendence results to the generalized non-periodic Thue-Morse sequence, we can found many transcendental numbers.

This paper has been withdrawn by the author. This article is included in my other article 'E. MIyanohara arXiv:1404.4153. Please ignore this article

Cited by in corpus (1)

• Transcendence of digital expansions and continued fractions generated by a cyclic permutation and $k$-adic expansion