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 A007490 Primes of form x^3 + y^3 + z^3 where x,y,z > 0. (Formerly M3036) 9
 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)
 OFFSET 1,1 COMMENTS 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 REFERENCES W. SierpiĆ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). 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. R. G. Wilson, V, Note, n.d. MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A003072 (all numbers). Sequence in context: A249374 A106085 A172487 * A173587 A022887 A063715 Adjacent sequences:  A007487 A007488 A007489 * A007491 A007492 A007493 KEYWORD nonn AUTHOR EXTENSIONS More terms from Vladimir Joseph Stephan Orlovsky, Mar 18 2010 Definition clarified by Charles R Greathouse IV, Sep 14 2015 STATUS approved

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Last modified December 14 07:15 EST 2018. Contains 318090 sequences. (Running on oeis4.)