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Kaprekar Number

Consider an $n$-digit number $k$. Square it and add the right $n$ digits to the left $n$ or $n-1$ digits. If the resultant sum is $k$, then $k$ is called a Kaprekar number. The first few are 1, 9, 45, 55, 99, 297, 703, ... (Sloane's A006886).

9^2=81 \qquad 8+1=9

297^2=88{,}209 \qquad 88+209=297.

See also Digital Root, Digitaddition, Happy Number, Kaprekar Routine, Narcissistic Number, Recurring Digital Invariant


Sloane, N. J. A. Sequence A006886/M4625 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein