The Beatty sequence is a spectrum sequence with an irrational base. In other words, the Beatty sequence corresponding to an irrational number θ is given by ⌊θ⌋, ⌊2θ⌋, ⌊3θ⌋, ..., where ⌊x⌋ is the floor function. If α and β are positive irrational numbers such that 1/α + 1/β = 1, then the Beatty sequences ⌊α⌋, ⌊2α⌋, ... and ⌊β⌋, ⌊2β⌋, ... together contain all the positive integers without repetition. The sequences for particular values of α and β are given in the following table, where ϕ is the golden ratio.

fractional part | Wythoff array | Wythoff's game