The Farey sequence of order n is the sequence of completely reduced fractions between 0 and 1 whose denominators do not exceed n, arranged in increasing order, starting with 0 (written 0/1) and ending with 1 (written 1/1). It is sometimes loosely called a Farey series, though that name is not strictly accurate since the sequence's terms are not summed.
Facts
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In Branch
Source Farey Sequence, from Wolfram MathWorld
Is Kind Of Object
Sources
1. Farey Sequence, from Wolfram MathWorld
References
Farey, J. 'On a Curious Property of Vulgar Fractions.' London, Edinburgh and Dublin Phil. Mag. 47, 385, 1816.
Definition
The Farey sequence F_n for any positive integer n is the set of irreducible rational numbers a/b with 0≤a≤b≤n and (a,b)=1 arranged in increasing order.
In Branch: Arithmetic, Subject classifications
Number Theory Arithmetic
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