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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| The sequence is complete. "In 1830, Legendre (1979) proved that every number larger than 1791 is a sum of four hexagonal numbers". See http://mathworld.wolfram.com/HexagonalNumber.html and reference : A.-M. Legendre, Theorie des nombres, 4th ed., 2 vols. Paris: A. Blanchard, 1979. It is easy to check all numbers <= 1791 by computer. - Olivier Pirson (olivier_pirson_opi(AT)yahoo.fr), Sep 14 2007
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REFERENCES
| R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Eric Weisstein's World of Mathematics, Hexagonal Number
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MATHEMATICA
| 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](* From Jean-François Alcover, Sep 21 2011 *)
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CROSSREFS
| Sequence in context: A189151 A120513 A004757 * A033894 A033649 A050680
Adjacent sequences: A007524 A007525 A007526 * A007528 A007529 A007530
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KEYWORD
| fini,nonn,full
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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