  The aim of this short note is to generalise the result of Rampersad--Shallit
saying that an automatic sequence and a Sturmian sequence cannot have
arbitrarily long common factors. We show that the same result holds if a
Sturmian sequence is replaced by an arbitrary sequence whose terms are given by
a generalised polynomial (i.e., an expression involving algebraic operations
and the floor function) that is not periodic except for a set of density zero.
