Examples
297 is a Kaprekar number for base 10, because 297² = 88209, which can be split into 88 and 209, and 88 + 209 = 297. By convention, the second part may start with the digit 0, but must be positive. For example, 999 is a Kaprekar number for base 10, because 999² = 998001, which can be split into 998 and 001, and 998 + 001 = 999. But 100 is not; although 100² = 10000 and 100 + 00 = 100, the second part here is not positive.
The first few Kaprekar numbers in base 10 are:
- 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999, 17344, 22222, 38962, 77778, 82656, 95121, 99999, 142857, 148149, 181819, 187110, 208495, 318682, 329967, 351352, 356643, 390313, 461539, 466830, 499500, 500500, 533170, ... (sequence A006886 in OEIS)
In particular, 9, 99, 999… are all Kaprekar numbers. More generally, for any base b, there exist infinitely many Kaprekar numbers, including all numbers of the form bn - 1.
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