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Kaprekar Number

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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. For example, 9 is a Kaprekar number since

9^2=81 8+1=9,

and 297 is a Kaprekar number since

297^2=88209 88+209=297.

The first few are 1, 9, 45, 55, 99, 297, 703, ... (OEIS A006886).

See also

Digital Root, Digitaddition, Happy Number, Kaprekar's Constant, Kaprekar Routine, Narcissistic Number, Recurring Digital Invariant

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References

Iannucci, D. E. "The Kaprekar Numbers." J. Integer Sequences 3, No. 00.1.2, 2000. http://www.math.uwaterloo.ca/JIS/VOL3/VOL3/iann2a.Kaprekar, D. "On Kaprekar Numbers." J. Rec. Math. 13, 81-82, 1980-1981.Sloane, N. J. A. Sequence A006886/M4625 in "The On-Line Encyclopedia of Integer Sequences."Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 73, 1986.

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Kaprekar Number

Cite this as:

Weisstein, Eric W. "Kaprekar Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KaprekarNumber.html

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