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The Collatz conjecture (or 3x+1 conjecture) is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937.
The conjecture can be summarized as follows.
Take any positive integer n. If n is even, divide it by 2 to get n / 2.
If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process indefinitely.
The conjecture is that no matter what number you start with, you will always eventually reach 1
6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:
1. Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)
2. Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2.
The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations.
This app gives you the detailed steps of computation for both the Collatz conhecture and Kaprekar number 6174.
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