Collatz Conjecture Lets Compute This

August 17, 2017 • Maths • 1 minutes to read • Edit

Before we look into what a Collatz conjecture is, I highly recommend watching the (below video by Numberphile.

Collatz conjecture also called as $3n+1$ problem, $3x+1$ mapping, Hasse’s algorithm, Kakutani’s problem, Syracuse algorithm, Syracuse problem, Thwaites conjecture, and Ulam’s problem.

Basically, the problem states that all positive whole numbers should eventually compute to $1$, which is based on the following condition:

$$ a_{n} = \begin{cases} \frac{1}{2}a_{n-1}, & \text{if $a_{n-1}$ is even} \\ 3n+1, & \text{if $a_{n-1}$ is odd} \end{cases} $$

The above equation says, at every iteration, check if the input number is even or odd. If the number is even then divide it by $2$ i.e., $\frac{number}{2}$ else multiply $3$ and add $1$ to the number i.e., $3 \ast number+1$.

Programmatically, this can be written as

def compute(number):

    while number != 1:
        print(number)
        if number % 2 == 0:
            number = (number / 2)
        else:
            number = int(3 * number + 1)
    else:
        print(number)

if __name__ == '__main__':
    compute(10)