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A053816
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Another version of the Kaprekar numbers: n such that n=q+r and n^2=q*10^m+r, for some m >= 1, q>=0 and 0<=r<10^m, with n != 10^a, a>=1. Here q and r must both be m-digit numbers.
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3
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1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4950, 5050, 7272, 7777, 9999, 17344, 22222, 77778, 82656, 95121, 99999, 142857, 148149, 181819, 187110, 208495, 318682, 329967, 351352, 356643, 390313, 461539, 466830, 499500, 500500, 533170
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OFFSET
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1,2
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COMMENTS
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Consider an m-digit number n. Square it and add the right m digits to the left m or m-1 digits. If the resultant sum is n, then n is a term of the sequence.
4879 and 5292 are in A006886 but not in this version.
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REFERENCES
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D. 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.
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LINKS
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Table of n, a(n) for n=1..36.
D. E. Iannucci, The Kaprekar numbers, J. Integer Sequences, Vol. 3, 2000, #1.2.
R. Munafo, Kaprekar Sequences
Eric Weisstein's World of Mathematics, Kaprekar Number
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EXAMPLE
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703 is Kaprekar because 703=494+209, 703^2=494209.
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MATHEMATICA
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kapQ[n_]:=Module[{idn2=IntegerDigits[n^2], len}, len=Length[idn2]; FromDigits[ Take[idn2, Floor[len/2]]]+FromDigits[Take[idn2, -Ceiling[len/2]]]==n]; Select[Range[540000], kapQ] (* From Harvey P. Dale, Aug 22 2011 *)
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CROSSREFS
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Cf. A037042, A053394, A053395, A053396, A053397, A045913, A003052.
Sequence in context: A087969 A044111 A006886 * A044492 A207359 A067536
Adjacent sequences: A053813 A053814 A053815 * A053817 A053818 A053819
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KEYWORD
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nonn,nice,base,easy
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AUTHOR
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Robert Munafo
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 11 2001
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STATUS
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approved
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