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A007490
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Primes of form x^3 + y^3 + z^3.
(Formerly M3036)
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4
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3, 17, 29, 43, 73, 127, 179, 197, 251, 277, 281, 307, 349, 359, 397, 433, 521, 547, 557, 577, 593, 701, 757, 811, 853, 857, 863, 881, 919, 953, 1009, 1051, 1091, 1217, 1249, 1367, 1459, 1483, 1559, 1583, 1637, 1753, 1801, 1861, 1907, 2017, 2027, 2069, 2087
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Heath-Brown shows that this sequence is infinite. [From Charles R Greathouse IV Jul 23 2009]
The definition implies x, y, z > 0, so the representation (x=0, y=z=1) for the prime 2 or the representation (x=-4, y=-2, z=5) for the prime 53 are not admitted. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2010]
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REFERENCES
| W. Sierpi\'{n}ski, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 108.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
D. R. Heath-Brown, Primes represented by x^3 + 2y^3. Acta Mathematica 186 (2001), pp. 1-84. [From Charles R Greathouse IV Jul 23 2009]
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MATHEMATICA
| lst={}; Do[Do[Do[p=n^3+m^3+k^3; If[PrimeQ[p], AppendTo[lst, p]], {n, 4!}], {m, 4!}], {k, 4!}]; Take[Union[lst], 36] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 23 2009]
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CROSSREFS
| Sequence in context: A105912 A106085 A172487 * A173587 A022887 A063715
Adjacent sequences: A007487 A007488 A007489 * A007491 A007492 A007493
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| More terms from Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 18 2010
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