A007490 Primes of form x^3 + y^3 + z^3 where x,y,z > 0. (Formerly M3036)

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

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. 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).

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

N. J. A. Sloane, Robert G. Wilson v

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Mar 18 2010

Definition clarified by Charles R Greathouse IV, Sep 14 2015

Status

approved