There is of course the silly implementation:
FareySequence[n_] := Union[Flatten[Table[j/i, {i, 1, n}, {j, 0, i}]]]
However, there are numerous properties and confinements of Farey sequences (that can be used, potentially, in an indirect manner).
This calls for a very simple, and, very efficient recurring/functional implementation, exhibiting Superiority. But I'm new to Mathematica and can't find the right combination of built-in functions, and pure functions..
Ideas?