mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
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):
|
|
"""
|
|
Collatz conjecture: start with any positive integer n.Next termis obtained from the previous term as follows:
|
|
if the previous term is even, the next term is one half the previous term.
|
|
If the previous term is odd, the next term is 3 times the previous term plus 1.
|
|
The conjecture states the sequence will always reach 1 regaardess of starting n.
|
|
Example:
|
|
>>> collatz_sequence(43)
|
|
[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]
|
|
"""
|
|
sequence = [n]
|
|
while n != 1:
|
|
if n % 2 == 0:# even
|
|
n //= 2
|
|
else:
|
|
n = 3*n +1
|
|
sequence.append(n)
|
|
return sequence
|
|
|
|
|
|
def main():
|
|
n = 43
|
|
sequence = collatz_sequence(n)
|
|
print(sequence)
|
|
print("collatz sequence from %d took %d steps."%(n,len(sequence)))
|
|
|
|
if __name__ == '__main__':
|
|
main()
|