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On patterns occurring in binary algebraic numbers
Author(s):
B.
Adamczewski;
N.
Rampersad
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3105-3109.
MSC (2000):
Primary 11J81, 68R15
Posted:
May 7, 2008
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Abstract:
We prove that every algebraic number contains infinitely many occurrences of  -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  or  in its ternary expansion.
References:
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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
DOI:
10.1090/S0002-9939-08-09319-2
PII:
S 0002-9939(08)09319-2
Received by editor(s):
July 19, 2007,
Received by editor(s) in revised form:
August 22, 2007
Posted:
May 7, 2008
Additional Notes:
The first author is supported by the ANR through the project ``DyCoNum''---JCJC06_134288
Communicated by:
Ken Ono
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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