On patterns occurring in binary algebraic numbers
Boris Adamczewski, Narad Rampersad · Proceedings of the American Mathematical Society · 2008
We prove that every algebraic number contains infinitely many occurrences of 7 / 3 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 010 010 or 02120 02120 in its ternary expansion.