Some Properties of Beatty Sequences I*
Ian G. Connell · Canadian Mathematical Bulletin · 1959
Two sequences of natural numbers are said to be complementary if they contain all the positive integers without repetition or omission. S. Beatty [l] observed that the sequences (1) (2) (where square brackets denote the integral part function) are complementary if and only if α > 0 and α is irrational. We call the pair (1),(2) Beatty sequences of argument α.