Initial data commit

Task/Farey-sequence/Sidef/farey-sequence.sidef

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+func farey_count(n) {   # A005728
+    1 + sum(1..n, {|k| euler_phi(k) })
+}
+
+func farey(n) {
+
+    var seq = [0]
+    var (a,b,c,d) = (0,1,1,n)
+
+    while (c <= n) {
+        var k = (n+b)//d
+        (a,b,c,d) = (c, d, k*c - a, k*d - b)
+        seq << a/b
+    }
+
+    return seq
+}
+
+say "Farey sequence for order 1 through 11 (inclusive):"
+for n in (1..11) {
+    say("F(%2d): %s" % (n, farey(n).map{.as_frac}.join(" ")))
+}
+
+say "\nNumber of fractions in the Farey sequence:"
+for n in (100..1000 -> by(100)) {
+    say ("F(%4d) =%7d" % (n, farey_count(n)))
+}