Definition:Kaprekar Number/Sequence

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Definition

The sequence of Kaprekar numbers begins:

$1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999, 17344, \ldots$

This sequence is A006886 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Some sources do not include such numbers as $4879$ and $5292$:

$1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4950, 5050, 7272, 7777, 9999, 17344, \ldots$

where the $2$nd of the $2$ parts begins with one or more leading zeroes:

$4879^2 = 23 \, 804 \, 641 \to 238 + 04641 = 4879$
$5292^2 = 28 \, 005 \, 264 \to 28 + 005264 = 5292$

This sequence is A053816 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Sources