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Kaprekar Number


A Kaprekar number is an n-digit positive integer k such that squaring it and adding the right n digits to the remaining left part (taken as 0 when empty) gives k. 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

Digitaddition, Digital Root, Happy Number, Kaprekar Routine, Kaprekar's Constant, 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. https://cs.uwaterloo.ca/journals/JIS/VOL3/iann2a.html.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 Resource. https://mathworld.wolfram.com/KaprekarNumber.html

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