Collatz Conjecture Calculator

The standard Collatz conjecture operates on any positive integer n using a simple conditional rule set. If the current number is even, you divide it by two (n / 2). If the current number is odd, you multiply it by three and add one (3n + 1). The conjecture posits that no matter which positive integer you start with, the sequence will eventually always fall into the repeating cycle of 4, 2, 1. The total number of steps required to reach the number one is known as the stopping time.

Let us compute the Collatz sequence for a starting value of N = 6. First, since 6 is even, we divide it by 2 to get 3. Next, 3 is odd, so we multiply by 3 and add 1, resulting in 10. Following this, 10 is even, yielding 5. For 5 (odd), we calculate 3(5) + 1 = 16. Then, 16 becomes 8, 8 becomes 4, 4 becomes 2, and finally 2 becomes 1. The complete sequence is 6, 3, 10, 5, 16, 8, 4, 2, 1, resulting in a stopping time of 8 steps.

When experimenting with different integer inputs, keep these strategies in mind. First, always verify that your starting number is a positive integer, as negative numbers and zero can introduce infinite loops or trivial fixed points. Second, pay close attention to peak values, as numbers can sometimes balloon significantly before eventually descending toward the final number one.