We can just take $A$ to be the set of numbers with an even number of ones in the binary expansion and $B$ the set of those with an odd number of ones. So $A=\{0,3,5,6,\dots\}$ and $B=\{1,2,4,7,\dots\}$. This is assuming $0 \in \mathbb{N}$. Otherwise just shift both sets by $1$. One possible proof that this works (and also a method to come up with this) is by considering the corresponding generating functions. This is in fact quite a classical trick.