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

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

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• nice

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.

Crossrefs

Cf. A000384 (hexagonal numbers).

Cf. A118278, A118279.

Programs

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

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 *)

Extensions

Corrected by T. D. Noe, Feb 14 2007