A213524 Numbers not representable as the sum of three octagonal numbers.

4, 5, 6, 7, 11, 12, 13, 14, 15, 18, 19, 20, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 38, 39, 44, 45, 46, 47, 51, 52, 53, 54, 55, 57, 58, 59, 60, 64, 68, 70, 71, 72, 75, 76, 77, 78, 79, 83, 84, 85, 89, 90, 91, 92, 93, 95, 99, 100, 102, 103, 108, 109, 110, 111

Offset: 1

Author

T. D. Noe, Jul 16 2012

Keywords

• nonn

Comments

There are an infinite number of numbers that are not the sum of three octagonal numbers.

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.

Crossrefs

Cf. A000567 (octagonal numbers).

Cf. A118278, A118279.

Programs

Mathematica

nn = 100; oct = Table[n*(3*n-2), {n, 0, nn}]; t = Table[0, {oct[[-1]]}]; Do[n = oct[[i]] + oct[[j]] + oct[[k]]; If[n <= oct[[-1]], t[[n]] = 1], {i, nn}, {j, i, nn}, {k, j, nn}]; Flatten[Position[t, 0]]