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

1,1

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.

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]]

Crossrefs

Cf. A000567 (octagonal numbers).

Cf. A118278, A118279.

Sequence in context: A356398 A364803 A022561 * A047312 A191164 A363089

Adjacent sequences: A213521 A213522 A213523 * A213525 A213526 A213527

Keyword

nonn

Author

T. D. Noe, Jul 16 2012

Status

approved