Definition:Farey Sequence/Order

Definition

Let $F_Q$ denote the Farey sequence of all reduced rational numbers with denominators not larger than $Q$:

$F_Q = \set {\dfrac p q: p = 0, \ldots, Q,\ q = 1, \ldots, Q,\ p \perp q}$

The index $Q$ is called the order of $F_Q$.

Also see

• Results about Farey sequences can be found here.

Source

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Farey sequence
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Farey sequence (of order $n$)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Farey sequence (of order $n$)