Returns the Farey sequence of order \(n\)
farey(n, print=FALSE, give.series = FALSE)
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
Boolean, with TRUE meaning to return the
series explicitly, and default FALSE meaning to return a 3
dimensional array as detailed below
Robin K. S. Hankin
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
G. H. Hardy and E. M. Wright 1985. An introduction to the theory of numbers, Oxford University Press (fifth edition)
unimodular