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?