Kaprekar number
In mathematics, a Kaprekar number , named after the Indian mathematician DR Kaprekar , is the base number a for a square number whose sequence of digits (in a number system based on b) can be divided into two parts that add up to the base number a.
Examples
The number 297 is a Kaprekar number with a base of 10; because 297² = 88209 and 297 = 88 + 209.
The second part of the number must be positive, but can contain one or more leading zeros. 999 is a Kaprekar number based on 10; because 999² = 998001 and 999 = 998 + 001 (= 1). However, 100 is not a Kaprekar number, although 100² = 10000 and 100 + 00 = 100, but the second part (00) is not positive.
Kaprekar numbers based on 10
The first base 10 Kaprekar numbers 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
The Kaprekar numbers must not start with the Kaprekar constant , e.g. B. 6174, can be confused.