S000809


Numbers that are not the sum of 3 generalized 10-gonal numbers.

4, 5, 6, 13, 16, 19, 25, 26, 31, 40, 43, 48, 57, 58, 70, 88, 109, 118, 141, 145, 151, 165, 226, 235, 250, 313, 316, 355, 391, 411, 420, 490, 580, 685, 736, 835, 1051, 1210, 1240, 1840, 1888, 1951, 3445, 3715, 5200

1

S000809

It appears that 5200 is the last number not representable as the sum of 3 generalized 10-gonal numbers.

T. D. Noe, Plot of 45 terms

Eric W. Weisstein, MathWorld: Polygonal Number

(Mma) f = 10; nn = 50; t = Table[k ((f - 2) k - (f - 4))/2, {k, -nn, nn}]; t2 = Select[Union[Flatten[Table[a + b + c, {a, t}, {b, t}, {c, t}]]], # <= t[[-1]] &]; Complement[Range[t[[-1]]], t2]

Cf. A118282S000806-S000819.

nonn,fini

T. D. Noe, Dec 28 2015

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