Initial data commit

Task/Farey-sequence/Lua/farey-sequence.lua

@@ -0,0 +1,19 @@
+-- Return farey sequence of order n
+function farey (n)
+    local a, b, c, d, k = 0, 1, 1, n
+    local farTab = {{a, b}}
+    while c <= n do
+        k = math.floor((n + b) / d)
+        a, b, c, d = c, d, k * c - a, k * d - b
+        table.insert(farTab, {a, b})
+    end
+    return farTab
+end
+
+-- Main procedure
+for i = 1, 11 do
+    io.write(i .. ": ")
+    for _, frac in pairs(farey(i)) do io.write(frac[1] .. "/" .. frac[2] .. " ") end
+    print()
+end
+for i = 100, 1000, 100 do print(i .. ": " .. #farey(i) .. " items") end