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A117089
Primes that are not the sum of 3 hexagonal numbers.
0
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.
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
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