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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 23 and 239 require 9 cubes and no numbers require > 9 cubes.
Sequence is conjectured to be complete.
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REFERENCES
| Bohman, Jan and Froberg, Carl-Erik; Numerical investigation of Waring's problem for cubes, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.
N. D. Elkies, Every even number greater than 454 is the sum of seven cubes, arXiv 1009.3983.
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
| Jean-Marc Deshouillers, Francois Hennecart and Bernard Landreau; appendix by I. Gusti Putu Purnaba, 7373170279850, Math. Comp. 69 (2000), 421-439.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Waring's Problem
Index entries for sequences related to sums of cubes
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EXAMPLE
| 239 = 1^3 + 4(2^3) + 3(3^3) + 5^3 - requires 9 cubes.
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MATHEMATICA
| 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 (noe(AT)sspectra.com), Sep 05 2006
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CROSSREFS
| Cf. A018889.
Sequence in context: A084931 A205597 A066758 * A115174 A092783 A108638
Adjacent sequences: A018885 A018886 A018887 * A018889 A018890 A018891
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KEYWORD
| fini,full,nonn
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AUTHOR
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Sep 05 2006
Corrected the definition (this question is still open). - N. J. A. Sloane, Sep 25 2011
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