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Define the sequences a_n, b_n, c_n as follows. a_0 = k, b_0 = 4, c_0 = 1.
If a_n is even then a_{n + 1} = \frac {a_n}{2}, b_{n + 1} = 2b_n, c_{n + 1} = c_n.
If a_n is odd, then a_{n + 1} = a_n - \frac {b_n}{2} - c_n, b_{n + 1} = b_n, c_{n + 1} = b_n + c_n.
Find the number of positive integers k < 1995 such that some a_n = 0.

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