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A007527
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Numbers that are not the sum of 4 hexagonal numbers.
(Formerly M3793)
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3
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5, 10, 11, 20, 25, 26, 38, 39, 54, 65, 70, 114, 130
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The sequence is complete. "In 1830, Legendre (1979) proved that every number larger than 1791 is a sum of four hexagonal numbers". See Eric Weisstein's link and Legendre reference. It is easy to check all numbers <= 1791 by computer. - Olivier Pirson, Sep 14 2007
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REFERENCES
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A.-M. Legendre, Theorie des nombres, 4th ed., 2 vols. Paris: A. Blanchard, 1979.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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lim = 1791; maxa = Ceiling[a /. Last[Solve[a(2a - 1) == lim]]]; t = Flatten[ Table[a(2a - 1) + b(2b - 1) + c(2c - 1) + d(2d - 1), {a, 0, maxa}, {b, 0, a}, {c, 0, b}, {d, 0, c}], 3]; Complement[ Range[lim], t](* Jean-François Alcover, Sep 21 2011 *)
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CROSSREFS
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KEYWORD
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fini,nonn,full
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AUTHOR
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STATUS
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approved
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