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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

Table of n, a(n) for n=1..13.

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-Fran├žois 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

N. J. A. Sloane

STATUS

approved

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