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A007527
Numbers that are not the sum of 4 hexagonal numbers.
3
5, 10, 11, 20, 25, 26, 38, 39, 54, 65, 70, 114, 130
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
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 315.
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
Nicholas John Bizzell-Browning, LIE scales: Composing with scales of linear intervallic expansion, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 143.
Shyam Sunder Gupta, Unlucky 13, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 13, 353-365.
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
KEYWORD
fini,nonn,full
STATUS
approved