A213523 Numbers not representable as the sum of three heptagonal numbers.

4, 5, 6, 10, 11, 12, 13, 16, 17, 22, 23, 24, 27, 28, 29, 30, 31, 33, 38, 39, 40, 44, 45, 46, 47, 49, 50, 51, 58, 60, 61, 64, 65, 66, 67, 71, 72, 76, 77, 78, 79, 84, 85, 87, 92, 93, 94, 97, 98, 101, 103, 104, 105, 108, 109, 118, 121, 124, 125, 127, 129, 132

Offset: 1

Author

T. D. Noe, Jul 16 2012

Keywords

• nonn
• fini

Comments

It is conjectured that 1348 positive numbers are not the sum of three heptagonal numbers.

References

• R. K. Guy, Unsolved Problems in Number Theory, D3.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1348
• R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.

Crossrefs

Cf. A000566 (heptagonal numbers).

Cf. A118278, A118279.

Programs

Mathematica

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]]