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A018888
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Write n = m_1^3 + ... +m_k^3 where the m_i are positive integers and k is minimal; sequence gives conjectured list of numbers for which k = 8 or 9.
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5
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15, 22, 23, 50, 114, 167, 175, 186, 212, 231, 238, 239, 303, 364, 420, 428, 454
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OFFSET
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1,1
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COMMENTS
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23 and 239 require 9 cubes and no numbers require > 9 cubes.
Sequence is conjectured to be complete.
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REFERENCES
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Bohman, Jan and Froberg, Carl-Erik; Numerical investigation of Waring's problem for cubes, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.
K. S. McCurley, An effective seven-cube theorem, J. Number Theory, 19 (1984), 176-183.
J. Roberts, Lure of the Integers, entry 239.
F. Romani, Computations concerning Waring's problem, Calcolo, 19 (1982), 415-431.
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LINKS
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Table of n, a(n) for n=1..17.
Jean-Marc Deshouillers, Francois Hennecart and Bernard Landreau; appendix by I. Gusti Putu Purnaba, 7373170279850, Math. Comp. 69 (2000), 421-439.
N. D. Elkies, Every even number greater than 454 is the sum of seven cubes, arXiv 1009.3983.
Eric Weisstein's World of Mathematics, Cubic Number
Eric Weisstein's World of Mathematics, Waring's Problem
Index entries for sequences related to sums of cubes
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EXAMPLE
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239 = 1^3 + 4(2^3) + 3(3^3) + 5^3 - requires 9 cubes.
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MATHEMATICA
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nn=10000; t=CoefficientList[Series[Sum[x^(k^3), {k, 0, Floor[nn^(1/3)]}]^7, {x, 0, nn}], x]; Flatten[Position[t, 0]]-1 - T. D. Noe, Sep 05 2006
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CROSSREFS
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Cf. A018889.
Sequence in context: A219214 A205597 A066758 * A115174 A092783 A108638
Adjacent sequences: A018885 A018886 A018887 * A018889 A018890 A018891
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KEYWORD
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fini,full,nonn
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AUTHOR
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Jud McCranie
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EXTENSIONS
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Corrected by T. D. Noe, Sep 05 2006
Corrected the definition (this question is still open). - N. J. A. Sloane, Sep 25 2011
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STATUS
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approved
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