maths.collatz_sequence¶
The Collatz conjecture is a famous unsolved problem in mathematics. Given a starting positive integer, define the following sequence: - If the current term n is even, then the next term is n/2. - If the current term n is odd, then the next term is 3n + 1. The conjecture claims that this sequence will always reach 1 for any starting number.
Other names for this problem include the 3n + 1 problem, the Ulam conjecture, Kakutani’s problem, the Thwaites conjecture, Hasse’s algorithm, the Syracuse problem, and the hailstone sequence.
Reference: https://en.wikipedia.org/wiki/Collatz_conjecture
Functions¶
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Generate the Collatz sequence starting at n. |
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Module Contents¶
- maths.collatz_sequence.collatz_sequence(n: int) collections.abc.Generator[int, None, None]¶
Generate the Collatz sequence starting at n. >>> tuple(collatz_sequence(2.1)) Traceback (most recent call last):
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Exception: Sequence only defined for positive integers >>> tuple(collatz_sequence(0)) Traceback (most recent call last):
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Exception: Sequence only defined for positive integers >>> tuple(collatz_sequence(4)) (4, 2, 1) >>> tuple(collatz_sequence(11)) (11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1) >>> tuple(collatz_sequence(31)) # doctest: +NORMALIZE_WHITESPACE (31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1) >>> tuple(collatz_sequence(43)) # doctest: +NORMALIZE_WHITESPACE (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)
- maths.collatz_sequence.main()¶