%I M3793 #19 Apr 20 2014 03:24:20
%S 5,10,11,20,25,26,38,39,54,65,70,114,130
%N Numbers that are not the sum of 4 hexagonal numbers.
%C 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
%D A.-M. Legendre, Theorie des nombres, 4th ed., 2 vols. Paris: A. Blanchard, 1979.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. K. Guy, <a href="http://www.jstor.org/stable/2324367">Every number is expressible as the sum of how many polygonal numbers?</a>, Amer. Math. Monthly 101 (1994), 169-172.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number</a>
%t 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 *)
%K fini,nonn,full
%O 1,1
%A _N. J. A. Sloane_