The automatic–generalised polynomial intersection conjecture

A sequence is generalised polynomial if it is obtained from polynomials by applying addition, multiplication, and the floor function, and it is ultimately periodic if it agrees with a periodic sequence outside a finite set. Automatic–generalised polynomial intersection conjecture. Suppose that a sequence $f$ is simultaneously automatic and generalised polynomial. Then $f$ is ultimately periodic. This conjecture concerns the intersection of automata-generated sequences with generalised polynomial sequences; the source presents it as the main motivation for the project, and no resolution is supplied here.