Kaprekar number

In mathematics, a Kaprekar number, named after the Indian mathematician DR Kaprekar, the base number a is a square number, the sequence of digits can be divided ( in a number system with base b ) in two parts, which added together give the basic number a. For example, the number 297 is a Kaprekar - number in base 10; because 297 ² = 88209 and 297 = 88 209 The second part number must be positive, but may contain one or more leading zeroes. So 999 is a Kaprekar - number in base 10; because 999 ² = 998 001; since this number can be in the figures 998 and 001 = 1 1 = 998, and divided into 999 100, however, is not Kaprekar number, although ² = 10000 and 100 100 00 = 100, but the second part (00) is not positive.

The first 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, 181 819, 187 110, 208495, 318682, 329967, 351 352, 356 643, 390 313, 461 539, 466 830, 499 500, 500 500, 533 170

The Kaprekar numbers may not be the Kaprekar constants, eg 6174, confused.