A "Kaprekar Number"  has an interesting property.  Think of a number k and count the number of digits n.  Then square the number k.  Using the square, add the right n digits to the remaining digits on the left.  If k results, you have found a Kaprekar Number.


The first Kraprekar numbers are 1, 9, 45, 55, 99, 297, 703, . . .

(Ex.  Let the number be 9.  Then 9 x 9= 81.  The original 9 is a one digit number.  Add the right 1 to the remaining 8.  Thus the number 9 is a Kaprekar.)