# Acknowledgments

## Acknowledgments

We would like to express our gratitude to Professor Vilmos Komornik who invite the author to visit the Department of Mathematics in University of Strasbourg. This work is done during the stay of the author in Strasbourg. We also express our gratitude to Dr. Timothy Foo (a researcher in School of Computing, National University of Singapore, Email: dcsfcht@nus.edu.sg) for sharing his finding. He gives the Theorem 4.4 with the proof and the Remark 4.5. We thank Professor Vilmos Komornik and Dr. Timothy Foo for discussing this question. And thanks Michel Marcus for giving me the link of OEIS A037178 and A256608.