A219726 Integers of the form x^3 + 2y^3 (x, y > 0).

3, 10, 17, 24, 29, 43, 55, 62, 66, 80, 81, 118, 127, 129, 136, 141, 155, 179, 192, 218, 232, 251, 253, 258, 270, 277, 314, 344, 345, 359, 375, 397, 433, 440, 459, 466, 471, 496, 514, 528, 557, 566, 593, 640, 648, 687, 694, 713, 731, 745, 750, 762, 775, 783

Offset: 1

Author

Zak Seidov, Nov 26 2012

Keywords

• nonn

Comments

D. R. Heath-Brown proved in 2001 that there are infinitely many prime numbers in this sequence. These primes are in A173587. - Bernard Schott, Apr 07 2020

Links

• Charles R Greathouse IV, 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.
• Wikipedia, Roger Heath-Brown

Crossrefs

Cf. A173587, A219722, A219725.

Programs

Mathematica

m = 10^3; Union[Flatten@Table[x^3 + 2 y^3, {x, m^(1/3)}, {y, ((m - x^3)/2)^(1/3)}]]

PARI

is(n)=for(y=1,sqrtnint((n-1)\2,3), if(ispower(n-2*y^3,3),return(1)));0 \\ Charles R Greathouse IV, Apr 07 2020

PARI

list(lim)=my(v=List(),Y); lim\=1; for(y=1,sqrtnint((lim-1)\2,3), Y=2*y^3; for(x=1,sqrtnint(lim-Y,3), listput(v,x^3+Y))); Set(v) \\ Charles R Greathouse IV, Apr 07 2020