Data commit

Task/Sylvesters-sequence/Python/sylvesters-sequence-1.py

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+'''Sylvester's sequence'''
+
+from functools import reduce
+from itertools import count, islice
+
+
+# sylvester :: [Int]
+def sylvester():
+    '''Non-finite stream of the terms
+       of Sylvester's sequence.
+       (OEIS A000058)
+    '''
+    def go(n):
+        return 1 + reduce(
+            lambda a, x: a * go(x),
+            range(0, n),
+            1
+        ) if 0 != n else 2
+
+    return map(go, count(0))
+
+
+# ------------------------- TEST -------------------------
+# main :: IO ()
+def main():
+    '''First terms, and sum of reciprocals.'''
+
+    print("First 10 terms of OEIS A000058:")
+    xs = list(islice(sylvester(), 10))
+    print('\n'.join([
+        str(x) for x in xs
+    ]))
+
+    print("\nSum of the reciprocals of the first 10 terms:")
+    print(
+        reduce(lambda a, x: a + 1 / x, xs, 0)
+    )
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()

Task/Sylvesters-sequence/Python/sylvesters-sequence-2.py

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+'''Sylvester's sequence'''
+
+from functools import reduce
+from itertools import islice
+
+# sylvester :: [Int]
+def sylvester():
+    '''A non finite sequence of the terms of OEIS A000058
+    '''
+    return iterate(
+        lambda x: x * (x - 1) + 1
+    )(2)
+
+
+# ------------------------- TEST -------------------------
+# main :: IO ()
+def main():
+    '''First terms, and sum of reciprocals.'''
+
+    print("First 10 terms of OEIS A000058:")
+    xs = list(islice(sylvester(), 10))
+    print('\n'.join([
+        str(x) for x in xs
+    ]))
+
+    print("\nSum of the reciprocals of the first 10 terms:")
+    print(
+        reduce(lambda a, x: a + 1 / x, xs, 0)
+    )
+
+# ----------------------- GENERIC ------------------------
+
+# iterate :: (a -> a) -> a -> Gen [a]
+def iterate(f):
+    '''An infinite list of repeated
+       applications of f to x.
+    '''
+    def go(x):
+        v = x
+        while True:
+            yield v
+            v = f(v)
+    return go
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()