Discovered by an Indian Mathematician in the 1950s, this series bears his name. He found that, given any 4-digit number, with distinct digits; on applying the Kaprekar process it will distill down to a single number - 6174 - called the Kaprekar constant.
The process is very simple.
Take any 4-digit number, say 1234.
Now write its digits in ascending and descending orders - 1234 and 4321 and subtract the two numbers so formed -
Repeat the above process and you get these numbers after each step:
1234 -> 3087 -> 8352 -> 6174 -> 6174 -> 6174
hmm. You see the pattern?
Similarly, if you take up a 3-digit number (with distinct digits), you'll end up with 495 on applying the Kaprekar process.
For 2-digit number, it gets interesting. You don't end up with one specific number, but a sequence of numbers!
09 -> 81 -> 63 -> 27 -> 45 -> 09
For higher number of digits, you typically end up in one of many sequences!
For 5-digits - it will be one of three sequences
For 6-digits - its either 631764, or 549945 or a sequence
For 7-digits - you'll end up in a sequence of 8 numbers
and so on ...
I have put the java code I used to generate the series, for public download at