More Information

The Collatz Conjecture is an unsolved problem in mathematics. The conjecture involves a sequence where you start at a number. To find the next number, you multiply it by 3 and add 1 when the number is odd, or you divide it by 2 if the number is even, and then repeat the process with the next number. The conjecture is that no matter what positive number you begin with, you will always eventually reach the loop of 1, 4, 2, 1.

This website was made utilizing a formula that will produce every possible loop, with the caveat that the addition can be any number instead of just +1, and the multiplier can be any number, not just 3.

The formula utilized does calculate every possible loop. However this website simplifies the formula in a few ways:
• This website only shows the loop in “smallest terms”
• This website only looks at loops where each segment of even numbers has a minimum size of 1 (or specifically, 1 + the number of times the multiplier is a factor of the divisor)

If you wish to learn more about the Collatz conjecture, I highly recommend watching Veritasium’s video on the subject: