Farey Fractions

The Farey Sequence, $F_{n}$ is the list of all simplified fractions between $\dfrac{0}{1}$ and $\dfrac{1}{1}$ with denominator less than or equal to $n$. For example,   $\large F_{5}=\dfrac{0}{1},\dfrac{1}{5},\dfrac{1}{4},\dfrac{1}{3},\dfrac{2}{5},\dfrac{1}{2},\dfrac{3}{5},\dfrac{2}{3},\dfrac{3}{4},\dfrac{4}{5},\dfrac{1}{1}$