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In mathematics, a non-negative integer is called a "Kaprekar number" for a given base if the representation of its square in that base can be split into two parts that add up to the original number, with the proviso that the part formed from the low-order digits of the square must be non-zero—although it is allowed to include leading zeroes. For instance, 45 is a Kaprekar number, because 562 =  2630 and 26 + 30 = 56. The number 1 is Kaprekar in every base, because 12 = 01 in any base, and   0 + 1 = 1. Kaprekar numbers are named after D. R. Kaprekar.

The Kaprekar numbers are 1, E, 56, 66, EE, 444, 778, EEE, 12XX, 1640, 2046, 2929, 3333, 4973, 5E60, 6060, 7249, 8889, 9293, 9E76, X580, X912, EEEE, 22223, 48730, 72392, 99999, EEEEE, 12E649, 16EX51, 1X1X1X, 222222, 22X54X, 26X952, 35186E, 39X39X, 404040, 4197X2, 450770, 5801E8, 5EE600, ...