A007536 Numbers that are not the sum of 3 hexagonal numbers (probably finite). (Formerly M3244)

4, 5, 9, 10, 11, 14, 19, 20, 23, 24, 25, 26, 32, 33, 37, 38, 39, 41, 42, 48, 50, 53, 54, 55, 59, 63, 64, 65, 69, 70, 76, 77, 80, 83, 85, 86, 89, 99, 102, 104, 108, 110, 113, 114, 115, 116, 123, 124, 128, 129, 130, 131, 140, 143, 144, 145, 146, 152, 161, 162, 167

Offset

1,1

Comments

Jud McCranie remarks that a(638) = 146858 is probably the last term.

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n=1..638

R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.

Mathematica

notSumQ[n_] := Reduce[0 <= x <= y <= z && n == x*(2x - 1) + y*(2y - 1) + z*(2z - 1), {x, y, z}, Integers] === False; A007536 = Reap[ Do[ If[notSumQ[n], Print[n]; Sow[n]], {n, 1, 135}]][[2, 1]] (* Jean-François Alcover, Jun 27 2012 *)

Prog

(MATLAB)
N = 10^7; % to get all terms up to N
M = floor((sqrt(1+8*N)+1)/4);
H = zeros(1, N);
H((1:M) .*(2*(1:M)-1)) = 1;
H2 = conv(H, H);
H2 = H2(1:N);
H3 = conv(H, H2);
HS = H(3:N) + H2(2:N-1) + H3(1:N-2);
find(HS==0) + 2 % Robert Israel, Jul 06 2016

Crossrefs

Cf. A000384 (hexagonal numbers).

Cf. A118278, A118279.

Sequence in context: A189136 A116026 A115915 * A209887 A064801 A109825

Adjacent sequences: A007533 A007534 A007535 * A007537 A007538 A007539

Keyword

nonn,fini,nice

Author

N. J. A. Sloane

Extensions

Corrected by T. D. Noe, Feb 14 2007

Status

approved