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%I M3036 #39 May 11 2021 09:04:22
%S 3,17,29,43,73,127,179,197,251,277,281,307,349,359,397,433,521,547,
%T 557,577,593,701,757,811,853,857,863,881,919,953,1009,1051,1091,1217,
%U 1249,1367,1459,1483,1559,1583,1637,1753,1801,1861,1907,2017,2027,2069,2087
%N Primes of form x^3 + y^3 + z^3 where x,y,z > 0.
%C Heath-Brown shows that this sequence is infinite. - _Charles R Greathouse IV_, Jul 23 2009
%C 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
%D W. Sierpiński, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 108.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A007490/b007490.txt">Table of n, a(n) for n = 1..10000</a>
%H D. R. Heath-Brown, <a href="https://doi.org/10.1007/BF02392715">Primes represented by x^3 + 2y^3</a>. Acta Mathematica 186 (2001), pp. 1-84.
%H R. G. Wilson, V, <a href="/A007490/a007490.pdf">Note, n.d.</a>
%t 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 *)
%o (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
%Y Cf. A003072 (all numbers).
%K nonn
%O 1,1
%A _N. J. A. Sloane_, _Robert G. Wilson v_
%E More terms from _Vladimir Joseph Stephan Orlovsky_, Mar 18 2010
%E Definition clarified by _Charles R Greathouse IV_, Sep 14 2015
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