A117089 Primes that are not the sum of 3 hexagonal numbers.

5, 11, 19, 23, 37, 41, 53, 59, 83, 89, 113, 131, 167, 173, 179, 229, 251, 269, 293, 313, 317, 383, 389, 439, 443, 509, 599, 641, 683, 859, 929, 1031, 1033, 1049, 1163, 1193, 1283, 1301, 1303, 1307, 1439, 1493, 1499, 1543, 1619, 1733, 2143, 2153, 2333, 2687, 2693, 3083, 3089, 3533, 3719, 3989, 4003, 4583, 4673, 4703, 5387, 5651, 5849, 5903, 6173, 6389, 6449, 7481, 9293, 12113, 15803, 16433, 19763, 61403

Offset

1,1

References

Legendre, Théorie des Nombres, 3rd edition, 1830.

Links

Table of n, a(n) for n=1..74.

W. Duke and R. Schulze-Pilot, Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids, Invent. Math. 99(1990), 49-57.

R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.

Formula

A000040 INTERSECT A007536.

Example

5 is the sum of five hexagonal numbers; 11 is the sum of six hexagonal numbers; the other 72 primes are the sum of four hexagonal numbers. - T. D. Noe, Apr 20 2006

Mathematica

nn=201; hex=Table[n(2n-1), {n, 0, nn-1}]; ps=Prime[Range[PrimePi[hex[[ -1]]]]]; Do[n=hex[[i]]+hex[[j]]+hex[[k]]; If[n<=hex[[ -1]]&&PrimeQ[n], ps=DeleteCases[ps, n]], {i, nn}, {j, i, nn}, {k, j, nn}]; ps (* T. D. Noe, Apr 20 2006 *)

Crossrefs

Cf. A000040, A000384, A007527, A007536, A117065.

Sequence in context: A320518 A084720 A032674 * A356140 A114269 A124855

Adjacent sequences: A117086 A117087 A117088 * A117090 A117091 A117092

Keyword

easy,fini,nonn

Author

Jonathan Vos Post, Apr 18 2006

Extensions

More terms from T. D. Noe, who conjectures that the list shown here is complete. His search up to 7*10^7 gave no further terms. - Apr 20 2006

Status

approved