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

1,1

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.

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]]

Crossrefs

Cf. A001107 (10-gonal numbers).

Cf. A118278, A118279.

Sequence in context: A161674 A285623 A213518 * A189481 A123977 A109602

Adjacent sequences: A214416 A214417 A214418 * A214420 A214421 A214422

Keyword

nonn,fini

Author

T. D. Noe, Jul 17 2012

Status

approved