Some thoughts
*11+22+33+44+55+66+77+88+99=495
*111+222+333+444+555+666+777+888+999+1110+69=6174
*6174+495=6669
*Square root of (1467,1476,1647,1674....) Only hole numbers 42 and 69. 42*42=1764 69*69=4761
* 69+42=111
* 0000,1111,2222,3333,4444,5555,6666,7777,8888,9999. 6174 should have a property similar from the rest of them.
(1467,1476,1674,1647 ...etc)/5555 -average of above, 6174 is 1,111. If variations are in order, 1,111 is in the middle of the variations.
* All numbers in Kaprekar process are divisible by 9.