A213525 Numbers not representable as the sum of three 9-gonal numbers.

4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 50, 51, 52, 53, 54, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 73, 74, 78, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 102, 103

Offset: 1

Author

T. D. Noe, Jul 16 2012

Keywords

• nonn
• fini

Comments

It is conjectured that 5282 positive numbers are not the sum of three 9-gonal numbers.

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..5282
• R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.

Crossrefs

Cf. A001106 (9-gonal numbers).

Cf. A118278, A118279.

Programs

Mathematica

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]]