Collatz 猜想和 Python

Python Day 4: Collatz Conjecture

原来总有学生问我，微积分有什么用啊， 我说如果微积分学好了，也许抽象代数和数论就能学好，那最后就能像Andrew Wiles 一样上 人物 年度杂志的封面了. (Andrew Wiles 证明了Fermat's Last Theorem，费玛大定理).

[caption id="attachment_1466" align="alignnone" width="300"]

z

ractapopulous / Pixabay[/caption]

数论里还有很多很容易了理解，但还没有证明的猜想,像 the Collatz 猜想.

Collatz Conjecture:

1. Take any natural number, n.
2. If n is even, divide it by 2.
3. Otherwise, n is odd. Multiply it by 3 and add 1
4. Repeat indefinitely, the number will converges to 1 for finitely many steps.

image

Mathematicians could not find a counterexample, however, there is no formal proof for Collatz Conjecture. Therefore the problem still remains unsolved.

I wrote short python code to test the algorithm, the numbers I checked did converge to 1.

But, as my maths professor always says:

"For example" is NOT a proof!
举例不是证明

def collatz_conjecture(x):
    lists= [x]
    if x<1 :
        return []
    while x > 1:
        if x% 2==0:
            x=x/2
        else:
            x=x*3+1
        lists.append(x)
    return(lists)

collatz_conjecture(6)
collatz_conjecture(93)
collatz_conjecture(180)

Output:

[6, 3.0, 10.0, 5.0, 16.0, 8.0, 4.0, 2.0, 1.0]

[93,280,140.0,70.0,35.0,106.0,53.0,160.0,80.0,40.0,20.0,10.0,5.0,16.0,8.0,4.0,2.0,1.0]

[180,90.0,45.0, 136.0,68.0,34.0,17.0,52.0,26.0,13.0,40.0,20.0,10.0,5.0,16.0,8.0,4.0,2.0,1.0]

Note: the picture is from https://xkcd.com/710/

**Happy Studying! **