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%I #9 Jul 06 2018 09:48:03
%S 4,5,6,10,11,12,13,16,17,22,23,24,27,28,29,30,31,33,38,39,40,44,45,46,
%T 47,49,50,51,58,60,61,64,65,66,67,71,72,76,77,78,79,84,85,87,92,93,94,
%U 97,98,101,103,104,105,108,109,118,121,124,125,127,129,132
%N Numbers not representable as the sum of three heptagonal numbers.
%C It is conjectured that 1348 positive numbers are not the sum of three heptagonal numbers.
%D R. K. Guy, Unsolved Problems in Number Theory, D3.
%H T. D. Noe, <a href="/A213523/b213523.txt">Table of n, a(n) for n = 1..1348</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 = 350; hep = Table[n*(5*n-3)/2, {n, 0, nn}]; t = Table[0, {hep[[-1]]}]; Do[n = hep[[i]] + hep[[j]] + hep[[k]]; If[n <= hep[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]
%Y Cf. A000566 (heptagonal numbers).
%Y Cf. A118278, A118279.
%K nonn,fini
%O 1,1
%A _T. D. Noe_, Jul 16 2012
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