In other words, given a sequence $(s_n)$, how can we tell if there exist irrationals $u>1$ and $v>1$ such that 

$$s_n = \lfloor un\rfloor +  \lfloor vn\rfloor$$

for every positive integer $n$?

A few thoughts:  Graham and Lin (*Math. Mag.* 51 (1978) 174-176) give a test for $(s_n)$ to be a single Beatty sequence $(\lfloor un\rfloor)$ (which they call the spectrum of $u$).  Perhaps someone knows a reference for a test for sums of two or more Beatty sequences?  A special case would be a test for a given sequence $(s_n)$ to be the sum of two *complementary* Beatty sequences (i.e., $1/u + 1/v = 1$).