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Search: id:A045913
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| A045913 |
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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. |
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+0
3
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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Powers of 10 were excluded in Kaprekar's original definition (A006886).
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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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D. E. Iannucci, The Kaprekar numbers, J. Integer Sequences, Vol. 3, 2000, #1.2.
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EXAMPLE
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703 is Kaprekar because 703=494+209, 703^2=494209. 100=100+0, 100^2=100^2+0.
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CROSSREFS
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Cf. A006886, A037042, A053394, A053395, A053396, A053397, A003052.
Adjacent sequences: A045910 A045911 A045912 this_sequence A045914 A045915 A045916
Sequence in context: A038206 A154389 A041172 this_sequence A156857 A037954 A041174
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KEYWORD
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nonn,nice,base,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 13 2001
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