Concept

# Farey sequence

Summary
In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted by the fraction 0/1, and ends with the value 1, denoted by the fraction 1/1 (although some authors omit these terms). A Farey sequence is sometimes called a Farey series, which is not strictly correct, because the terms are not summed. Examples The Farey sequences of orders 1 to 8 are : :F1 = { 0/1, 1/1 } :F2 = { 0/1, 1/2, 1/1 } :F3 = { 0/1, 1/3, 1/2, 2/3, 1/1 } :F4 = { 0/1, 1/4, 1/3, 1/2, 2/3, 3/4,
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