A214419 Numbers not representable as the sum of three 10-gonal numbers.

4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 56, 57, 58, 59, 60, 61, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 82, 83, 84, 88, 90, 91, 92, 93, 94, 97, 98

Offset: 1

Author

T. D. Noe, Jul 17 2012

Keywords

• nonn
• fini

Comments

It is conjectured that 7687 positive numbers are not the sum of three 10-gonal numbers.

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..7687
• R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.
• R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.

Crossrefs

Cf. A001107 (10-gonal numbers).

Cf. A118278, A118279.

Programs

Mathematica

nn = 750; dec = Table[n*(4*n-3), {n, 0, nn}]; t = Table[0, {dec[[-1]]}]; Do[n = dec[[i]] + dec[[j]] + dec[[k]]; If[n <= dec[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]