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A045913 Kaprekar numbers, allowing powers of 10: n such that n=q+r and n^2=q*10^m+r, for some m >= 1, q>=0 and 0<=r<10^m. Here q and r must both be m-digit numbers. 6
1, 9, 10, 45, 55, 99, 100, 297, 703, 999, 1000, 2223, 2728, 4950, 5050, 7272, 7777, 9999, 10000, 17344, 22222, 77778, 82656, 95121, 99999, 100000, 142857, 148149, 181819, 187110, 208495, 318682, 329967, 351352, 356643, 390313, 461539, 466830 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Powers of 10 were excluded in Kaprekar's original definition (A006886).

REFERENCES

D. R. Kaprekar, On Kaprekar numbers, J. Rec. Math., 13 (1980-1981), 81-82.

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 151.

LINKS

Table of n, a(n) for n=1..38.

D. E. Iannucci, The Kaprekar numbers, J. Integer Sequences, Vol. 3, 2000, #1.2.

Rosetta Code, Kaprekar numbers

Wikipedia, Kaprekar_number

Eric Weisstein's World of Mathematics, Kaprekar Number

Index entries for Colombian or self numbers and related sequences

EXAMPLE

703 is Kaprekar because 703=494+209, 703^2=494209. 100=100+0, 100^2=100^2+0.

CROSSREFS

Cf. A006886, A037042, A053394, A053395, A053396, A053397, A003052.

Sequence in context: A154389 A041172 A248353 * A156857 A259914 A037954

Adjacent sequences:  A045910 A045911 A045912 * A045914 A045915 A045916

KEYWORD

nonn,nice,base,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org), Apr 13 2001

Definition clarified by Reinhard Zumkeller, Oct 05 2014

STATUS

approved

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Last modified May 26 18:58 EDT 2017. Contains 287129 sequences.