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Task/Stern-Brocot-sequence/Python/stern-brocot-sequence-1.py

@@ -0,0 +1,36 @@
+def stern_brocot(predicate=lambda series: len(series) < 20):
+    """\
+    Generates members of the stern-brocot series, in order, returning them when the predicate becomes false
+
+    >>> print('The first 10 values:',
+              stern_brocot(lambda series: len(series) < 10)[:10])
+    The first 10 values: [1, 1, 2, 1, 3, 2, 3, 1, 4, 3]
+    >>>
+    """
+
+    sb, i = [1, 1], 0
+    while predicate(sb):
+        sb += [sum(sb[i:i + 2]), sb[i + 1]]
+        i += 1
+    return sb
+
+
+if __name__ == '__main__':
+    from fractions import gcd
+
+    n_first = 15
+    print('The first %i values:\n  ' % n_first,
+          stern_brocot(lambda series: len(series) < n_first)[:n_first])
+    print()
+    n_max = 10
+    for n_occur in list(range(1, n_max + 1)) + [100]:
+        print('1-based index of the first occurrence of %3i in the series:' % n_occur,
+              stern_brocot(lambda series: n_occur not in series).index(n_occur) + 1)
+              # The following would be much faster. Note that new values always occur at odd indices
+              # len(stern_brocot(lambda series: n_occur != series[-2])) - 1)
+
+    print()
+    n_gcd = 1000
+    s = stern_brocot(lambda series: len(series) < n_gcd)[:n_gcd]
+    assert all(gcd(prev, this) == 1
+               for prev, this in zip(s, s[1:])), 'A fraction from adjacent terms is reducible'

Task/Stern-Brocot-sequence/Python/stern-brocot-sequence-2.py

@@ -0,0 +1,22 @@
+>>> from itertools import takewhile, tee, islice
+>>>  from collections import deque
+>>> from fractions import gcd
+>>>
+>>> def stern_brocot():
+    sb = deque([1, 1])
+    while True:
+        sb += [sb[0] + sb[1], sb[1]]
+        yield sb.popleft()
+
+
+>>> [s for _, s in zip(range(15), stern_brocot())]
+[1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4]
+>>> [1 + sum(1 for i in takewhile(lambda x: x != occur, stern_brocot()))
+     for occur in (list(range(1, 11)) + [100])]
+[1, 3, 5, 9, 11, 33, 19, 21, 35, 39, 1179]
+>>> prev, this = tee(stern_brocot(), 2)
+>>> next(this)
+1
+>>> all(gcd(p, t) == 1 for p, t in islice(zip(prev, this), 1000))
+True
+>>>