%I
%S 4,5,6,7,11,12,13,14,15,18,19,20,25,26,27,28,31,32,33,34,35,36,38,39,
%T 44,45,46,47,51,52,53,54,55,57,58,59,60,64,68,70,71,72,75,76,77,78,79,
%U 83,84,85,89,90,91,92,93,95,99,100,102,103,108,109,110,111
%N Numbers not representable as the sum of three octagonal numbers.
%C There are an infinite number of numbers that are not the sum of three octagonal numbers.
%D R. K. Guy, Unsolved Problems in Number Theory, D3.
%H T. D. Noe, <a href="/A213524/b213524.txt">Table of n, a(n) for n = 1..10000</a>
%H R. K. Guy, <a href="https://www.jstor.org/stable/2324367">Every number is expressible as the sum of how many polygonal numbers?</a>, Amer. Math. Monthly 101 (1994), 169172.
%t nn = 100; oct = Table[n*(3*n2), {n, 0, nn}]; t = Table[0, {oct[[1]]}]; Do[n = oct[[i]] + oct[[j]] + oct[[k]]; If[n <= oct[[1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]
%Y Cf. A000567 (octagonal numbers).
%Y Cf. A118278, A118279.
%K nonn
%O 1,1
%A _T. D. Noe_, Jul 16 2012
