val farey = fn(n number) {
    var a, b, c, d = 0, 1, 1, n
    while[=[[0, 1]]] c <= n {
        val k = (n + b) // d
        a, b, c, d = c, d, k * c - a, k * d - b
        _while ~= [[a, b]]
    }
}

val testFarey = fn*() {
    writeln "Farey sequence for orders 1 through 11"
    for i of 11 {
        writeln "{{i:2}}: ", join(map(farey(i), by=fn(f) { "{{f[1]}}/{{f[2]}}" }), delim=" ")
    }
}

testFarey()

writeln()
writeln "count of Farey sequence fractions for 100 to 1000 by hundreds"
for i = 100; i <= 1000; i += 100 {
    writeln "{{i:4}}: ", len(farey(i))
}