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 A007527 Numbers that are not the sum of 4 hexagonal numbers. (Formerly M3793) 3
 5, 10, 11, 20, 25, 26, 38, 39, 54, 65, 70, 114, 130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 REFERENCES 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). LINKS R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172. Eric Weisstein's World of Mathematics, Hexagonal Number 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](* Jean-François Alcover, Sep 21 2011 *) CROSSREFS Sequence in context: A189151 A120513 A004757 * A033894 A033649 A271922 Adjacent sequences:  A007524 A007525 A007526 * A007528 A007529 A007530 KEYWORD fini,nonn,full AUTHOR STATUS approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)