Initial data commit

Task/Farey-sequence/Python/farey-sequence-1.py

@@ -0,0 +1,21 @@
+from fractions import Fraction
+
+
+class Fr(Fraction):
+    def __repr__(self):
+        return '(%s/%s)' % (self.numerator, self.denominator)
+
+
+def farey(n, length=False):
+    if not length:
+        return [Fr(0, 1)] + sorted({Fr(m, k) for k in range(1, n+1) for m in range(1, k+1)})
+    else:
+        #return 1         +    len({Fr(m, k) for k in range(1, n+1) for m in range(1, k+1)})
+        return  (n*(n+3))//2 - sum(farey(n//k, True) for k in range(2, n+1))
+
+if __name__ == '__main__':
+    print('Farey sequence for order 1 through 11 (inclusive):')
+    for n in range(1, 12):
+        print(farey(n))
+    print('Number of fractions in the Farey sequence for order 100 through 1,000 (inclusive) by hundreds:')
+    print([farey(i, length=True) for i in range(100, 1001, 100)])