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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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10
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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
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OFFSET
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1,1
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COMMENTS
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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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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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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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