Generalized Beatty sequences and complementary triples

J. -P. Allouche, F. M. Dekking

A generalized Beatty sequence is a sequence $V$ defined by $V(n)=p\lfloor n\alpha \rfloor +qn+r$, for $n=1,2,\dots$, where $\alpha$ is a real number, and $p,q,r$ are integers. These occur in…