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Search: id:A117089
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| A117089 |
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Primes that are that are not the sum of 3 hexagonal numbers. |
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1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 (noe(AT)sspectra.com), Apr 20 2006
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REFERENCES
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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.
Legendre, Theorie des Nombres, 3rd edition, 1830.
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FORMULA
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A000040 INTERSECT A007536.
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MATHEMATICA
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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 (noe(AT)sspectra.com), Apr 20 2006
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CROSSREFS
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Cf. A000040, A000384, A007527, A007536, A117065.
Sequence in context: A084720 A032674 A100141 this_sequence A114269 A124855 A022823
Adjacent sequences: A117086 A117087 A117088 this_sequence A117090 A117091 A117092
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KEYWORD
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easy,fini,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 18 2006
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), who conjectures that the list shown here is complete. His computer has searched out to 7*10^7 without finding further terms.- Apr 20 2006
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