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On patterns occurring in binary algebraic numbers

Authors: B. Adamczewski and N. Rampersad
Journal: Proc. Amer. Math. Soc. 136 (2008), 3105-3109
MSC (2000): Primary 11J81, 68R15
Published electronically: May 7, 2008
MathSciNet review: 2407073
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Abstract: We prove that every algebraic number contains infinitely many occurrences of $ 7/3$-powers in its binary expansion. Using the same approach, we also show that every algebraic number contains either infinitely many occurrences of squares or infinitely many occurrences of one of the blocks $ 010$ or $ 02120$ in its ternary expansion.

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Additional Information

B. Adamczewski
Affiliation: CNRS, Université Lyon 1, Université de Lyon, Institut Camille Jordan, 21 avenue Claude Bernard, 69622 Villeurbanne cedex, France

N. Rampersad
Affiliation: School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Received by editor(s): July 19, 2007
Received by editor(s) in revised form: August 22, 2007
Published electronically: May 7, 2008
Additional Notes: The first author is supported by the ANR through the project “DyCoNum”—JCJC06_{1}34288
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.