# farey

##### Farey sequences

Returns the Farey sequence of order \(n\)

- Keywords
- array

##### Usage

`farey(n, print=FALSE, give.series = FALSE)`

##### Arguments

- n
Order of Farey sequence

Boolean, with

`TRUE`

meaning to print out the text version of the Farey sequence in human-readable form. Default value of`FALSE`

means not to print anything- give.series
Boolean, with

`TRUE`

meaning to return the series explicitly, and default`FALSE`

meaning to return a 3 dimensional array as detailed below

##### Details

If `give.series`

takes its default value of `FALSE`

, return
a matrix `a`

of dimension `c(2,u)`

where `u`

is a
(complicated) function of `n`

. If `v <- a[i,]`

, then
`v[1]/v[2]`

is the \(i^{\mathrm{th}}\) term of the Farey
sequence. Note that `det(a[(n):(n+1),])== -1`

If `give.series`

is `TRUE`

, then return a matrix `a`

of
size `c(4,u-1)`

. If `v <- a[i,]`

, then `v[1]/v[2]`

and
`v[3]/v[4]`

are successive pairs of the Farey sequence. Note
that `det(matrix(a[,i],2,2))== -1`

##### References

G. H. Hardy and E. M. Wright 1985. *An introduction to the
theory of numbers*, Oxford University Press (fifth edition)

##### See Also

##### Examples

```
# NOT RUN {
farey(3)
# }
```

*Documentation reproduced from package elliptic, version 1.4-0, License: GPL-2*