SOLVED
Is the set of odd integers not of the form $2^k+p$ the union of an infinite arithmetic progression and a set of density $0$?
Erdős called this conjecture 'rather silly'. Using covering congruences Erdős
[Er50] proved that the set of such odd integers contains an infinite arithmetic progression.
Chen [Ch23] has proved the answer is no.
See also [9], [10], and [11].
