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

1,1

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A173587, A219722, A219725.

Sequence in context: A003072 A025395 A047702 * A017017 A297665 A309347

Adjacent sequences: A219723 A219724 A219725 * A219727 A219728 A219729

Keyword

nonn

Author

Zak Seidov, Nov 26 2012

Status

approved