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Search: id:A006886
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| A006886 |
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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.
(Formerly M4625)
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+0
13
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| 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999, 17344, 22222, 38962, 77778, 82656, 95121, 99999, 142857, 148149, 181819, 187110, 208495, 318682, 329967, 351352, 356643, 390313, 461539, 466830, 499500, 500500, 533170
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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4879 and 5292 are in this sequence but not in A053816.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Kaprekar, On Kaprekar numbers, J. Rec. Math., 13 (1980-1981), 81-82.
Douglas E. Iannucci and Bertrum Foster, Kaprekar Triples, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.8.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 151.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1019
D. E. Iannucci, Journal of Integer Sequences, Vol. 3, 2000, #1.2, The Kaprekar Numbers
W. Schneider, Kaprekar Numbers
G. Villemin's Almanach of Numbers, Procede de Kaprekar
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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703 is Kaprekar because 703=494+209, 703^2=494209.
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CROSSREFS
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See A053816 for another version.
Cf. A037042, A053394, A053395, A053396, A053397, A045913, A003052.
Sequence in context: A124983 A087969 A044111 this_sequence A053816 A044492 A067536
Adjacent sequences: A006883 A006884 A006885 this_sequence A006887 A006888 A006889
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KEYWORD
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nonn,nice,base,easy
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AUTHOR
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mrob(AT)mrob.com (Robert P Munafo)
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 11 2001
4879 and 5292 added by Larry Reeves (larryr(AT)acm.org), Apr 24, 2001
38962 added by Larry Reeves (larryr(AT)acm.org), May 23 2002
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