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A007490
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Primes of form x^3 + y^3 + z^3 where x,y,z > 0.
(Formerly M3036)
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9
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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;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Heath-Brown shows that this sequence is infinite. - 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. - R. J. Mathar, Mar 19 2010
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REFERENCES
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W. Sierpiński, 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
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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.
R. G. Wilson, V, Note, n.d.
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MATHEMATICA
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nn = 3000; Select[Union[Flatten[Table[x^3 + y^3 + z^3, {x, nn^(1/3)}, {y, x, (nn - x^3)^(1/3)}, {z, y, (nn - x^3 - y^3)^(1/3)}]]], PrimeQ] (* T. D. Noe, Sep 18 2012 *)
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PROG
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(PARI) list(lim)=my(v=List(), k, t); lim\=1; for(x=1, sqrtnint(lim-2, 3), for(y=1, min(sqrtnint(lim-x^3-1, 3), x), k=x^3+y^3; for(z=1, min(sqrtnint(lim-k, 3), y), if(isprime(t=k+z^3), listput(v, t))))); Set(v) \\ Charles R Greathouse IV, Sep 14 2015
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CROSSREFS
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Cf. A003072 (all numbers).
Sequence in context: A249374 A106085 A172487 * A173587 A022887 A063715
Adjacent sequences: A007487 A007488 A007489 * A007491 A007492 A007493
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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EXTENSIONS
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More terms from Vladimir Joseph Stephan Orlovsky, Mar 18 2010
Definition clarified by Charles R Greathouse IV, Sep 14 2015
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STATUS
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approved
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