The Kaprekar constant $K_k$ in a given base $b$ is a $k$ digit number $K$ such that subjecting any other $k$ digit number $n$ (except the repunit $R_k$ and numbers with $k - 1$ repeated digits) to the following process:

1. Arrange the digits of $n$ in ascending order, forming the $k$ digit number $a$ and then in descending order, forming the $k$ digit number $b$

2. If $a > b$ calculate $a - b = c$ otherwise $b - a = c$

3. Goto step 1 using $c$ instead of $n$

eventually gives $K$ (This process is sometimes called the Kaprekar routine).

For $b = 10$ the Kaprekar constant for $k = 4$ is 6174. Using $n = 1729$ we find that 9721 - 1279 gives 8442. Then 8442 - 2448 = 5994. Then 9954 - 4599 gives 5355. Then 5553 - 3555 gives 1998. Then 9981 - 1899 gives 8082. Then 8820 - 288 gives 8532. Then 8532 - 2538 finally gives 6174. (Some numbers take longer than others). $K_2$ and $K_7$ don't exist for $b = 10$