turkmath.org

The Beatty Sequence generated by an irrational r>1 is ([nr] : n>0), where [c] denotes the integer part of a real number c. A well-known property of this sequence is that "any pattern that appears once has to appear infinitely many times; moreover we may determine when a pattern appears next time with a small error". After explaining what this means, we will present the proof of a strengthening of it. Our proof depends on the model theoretic study of the sequence and all the necessary background will be overviewed. (This is a joint work with Melissa Özsahakyan.)