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9c0cbe3307
* Create collatz_sequence.py * Update and rename collatz_sequence.py to maths/collatz_sequence.py * doctest
29 lines
932 B
Python
29 lines
932 B
Python
def collatz_sequence(n):
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"""
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Collatz conjecture: start with any positive integer n.Next termis obtained from the previous term as follows:
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if the previous term is even, the next term is one half the previous term.
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If the previous term is odd, the next term is 3 times the previous term plus 1.
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The conjecture states the sequence will always reach 1 regaardess of starting n.
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Example:
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>>> collatz_sequence(43)
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[43, 130, 65, 196, 98, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1]
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"""
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sequence = [n]
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while n != 1:
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if n % 2 == 0:# even
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n //= 2
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else:
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n = 3*n +1
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sequence.append(n)
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return sequence
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def main():
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n = 43
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sequence = collatz_sequence(n)
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print(sequence)
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print("collatz sequence from %d took %d steps."%(n,len(sequence)))
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if __name__ == '__main__':
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main()
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