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Search: id:A047696
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| A047696 |
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Smallest positive number that can be written in n ways as a sum of two (not necessarily positive) cubes. |
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+0
4
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| 1, 91, 728, 2741256, 6017193, 1412774811, 11302198488, 137513849003496, 424910390480793000, 933528127886302221000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sometimes called cab-taxi (or cabtaxi) numbers.
Christian Boyer: After his recent work on Taxicab(6) confirming the number found as an upper bound by Randall Rathbun in 2002, Uwe Hollerbach (USA) confirmed this week that my upper bound constructed in Dec 2006 is really Cabtaxi(10). See his announcement. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 08 2008
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REFERENCES
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C. Boyer, "Les nombres Taxicabs", in Dossier Pour La Science, pp. 26-28, Volume 59 (Jeux math') April/June 2008 Paris.
R. K. Guy, Unsolved Problems in Number Theory, Section D1.
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LINKS
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D. J. Bernstein, Enumerating solutions to p(a) + q(b) = r(c) + s(d)
D. J. Bernstein, Enumerating solutions to p(a) + q(b) = r(c) + s(d)
C. Boyer, New upper bounds on Taxicab and Cabtaxi numbers
Uwe Hollerbach, The tenth cabtaxi number is 933528127886302221000, May 14, 2008.
Eric Weisstein's World of Mathematics, Taxicab Numbers
Eric Weisstein's World of Mathematics, Cabtaxi Number
Wikipedia, Cabtaxi number
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EXAMPLE
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91 = 6^3 - 5^3 = 4^3 + 3^3 (in two ways).
Cabtaxi(9)=424910390480793000 = 645210^3 + 538680^3 = 649565^3 + 532315^3 = 752409^3 - 101409^3 = 759780^3 - 239190^3 = 773850^3 - 337680^3 = 834820^3 - 539350^3 = 1417050^3 - 1342680^3 = 3179820^3 - 3165750^3 = 5960010^3 - 5956020^3.
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CROSSREFS
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Cf. A011541, A047697.
Cf. A011541, A047697.
Sequence in context: A165220 A020218 A084319 this_sequence A043459 A038488 A072393
Adjacent sequences: A047693 A047694 A047695 this_sequence A047697 A047698 A047699
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KEYWORD
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nonn,nice,hard
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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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a(9) from Duncan Moore (Duncan.Moore(AT)nnc.co.uk), Feb 01 2005. This term was found on Jan 31 2005.
For a(10), see the C. Boyer link.
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