# The Haros-Farey sequence at two hundred years. A survey.

@inproceedings{Cobeli2003TheHS, title={The Haros-Farey sequence at two hundred years. A survey.}, author={Cristian Cobeli and Alexandru Zaharescu}, year={2003} }

Let be the set of representatives for the nonnegative subunitary rational numbers in their lowest terms with denominators at most and arranged in ascending order. This finite sequence of fractions has two remarkable basic properties. The first one asserts that the difference between two consecutive fractions equals the inverse of the product of their denominators. The second, called also the mediant property, says that if , and are consecutive in then . These properties are equivalent and they…

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