English

Digital pattern and transcendence via generalized $k$-regular sequences

Number Theory 2021-12-13 v3 Combinatorics

Abstract

In this paper, we prove that there are uncountable many real transcendental numbers, which are generated by digital pattern sequences. This generalizes the main theorem in Morton and Mourant, which states the existence of countable many similar numbers. Our method relies on the combinatorial quantitative transcendence criterion established by Adamczewski and Bugeaud and properties of generalized k-regular sequences, which is introduced by this paper.

Cite

@article{arxiv.1809.09320,
  title  = {Digital pattern and transcendence via generalized $k$-regular sequences},
  author = {Eiji Miyanohara},
  journal= {arXiv preprint arXiv:1809.09320},
  year   = {2021}
}

Comments

Title change. We unifies the arXiv:1809.09320v2 and arXiv:1405.7124v6

R2 v1 2026-06-23T04:17:23.668Z