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%I #9 Jul 06 2018 09:47:49
%S 4,5,6,7,8,12,13,14,15,16,17,20,21,22,23,28,29,30,31,32,35,36,37,38,
%T 39,40,41,43,44,45,50,51,52,53,54,58,59,60,61,62,63,65,66,67,68,69,73,
%U 74,78,80,81,82,83,86,87,88,89,90,91,95,96,97,98,102,103
%N Numbers not representable as the sum of three 9-gonal numbers.
%C It is conjectured that 5282 positive numbers are not the sum of three 9-gonal numbers.
%D R. K. Guy, Unsolved Problems in Number Theory, D3.
%H T. D. Noe, <a href="/A213525/b213525.txt">Table of n, a(n) for n = 1..5282</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), 169-172.
%t nn = 700; non = Table[n*(7*n - 5)/2, {n, 0, nn}]; t = Table[0, {non[[-1]]}]; Do[n = non[[i]] + non[[j]] + non[[k]]; If[n <= non[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]
%Y Cf. A001106 (9-gonal numbers).
%Y Cf. A118278, A118279.
%K nonn,fini
%O 1,1
%A _T. D. Noe_, Jul 16 2012
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