naive 64 - floating point problem

064.py

@@ -0,0 +1,39 @@
+from math import sqrt
+
+
+def step(value):
+    return int(value), ( value + int(value) ) / (value ** 2 - int(value) ** 2)
+
+def recursion(value, seen=[]):
+    integer, new = step(value)
+    # floating point precision an issue must truncate/round
+    # 3 was chosen empirically 10 ** -4 precision in assessing periodicity
+    truncated = round(new, 1)
+    if truncated in seen:
+        return len(seen)
+    return recursion(new, seen + [truncated])
+
+def period(N):
+    """
+    >>> [period(n) for n in (2, 3, 5, 6, 7, 8, 10, 11, 12, 13)]
+    [1, 2, 1, 2, 4, 2, 1, 2, 2, 5]
+    >>> period(23)
+    4
+    """
+    value = sqrt(N)
+    if int(value)==value:
+        return 0
+    return recursion(sqrt(N))
+
+def solution(max):
+    """
+    >>> solution(13)
+    4
+    """
+    return sum(1 for n in range(2, max + 1) if period(n) % 2 != 0)
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+
+print solution(10000)