Any positive integer is a Kaprekar number on the following conditions: the integer is 1 or when splitting the integer's square in two makes their sum equal the original integer.

For example, the square of 55 equals 3,025. Splitting the square in 30 and 25 makes their sum equal 55. Both operands must not equal zero, and must retain their digit order, but they may differ in length.

Print all the Kaprekar numbers from 1 to 25,000,000 inclusive, each on their own line.

External links: OEIS A006886, Rosetta Code, Wikipedia