def farey( n ) =
  res = seq()
  a, b, c, d = 0, 1, 1, n
  res += "$a/$b"

  while c <= n
    k = (n + b)\d
    a, b, c, d = c, d, k*c - a, k*d - b
    res += "$a/$b"

for i <- 1..11
  println( "$i: ${farey(i).mkString(', ')}" )

for i <- 100..1000 by 100
  println( "$i: ${farey(i).length()}" )