cp's OEIS Frontend

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

%I A219726 #19 Apr 07 2020 22:10:31
%S A219726 3,10,17,24,29,43,55,62,66,80,81,118,127,129,136,141,155,179,192,218,
%T A219726 232,251,253,258,270,277,314,344,345,359,375,397,433,440,459,466,471,
%U A219726 496,514,528,557,566,593,640,648,687,694,713,731,745,750,762,775,783
%N A219726 Integers of the form x^3 + 2y^3 (x, y > 0).
%C A219726 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
%H A219726 Charles R Greathouse IV, <a href="/A219726/b219726.txt">Table of n, a(n) for n = 1..10000</a>
%H A219726 D. R. Heath-Brown, <a href="https://projecteuclid.org/euclid.acta/1485891369">Primes represented by x^3 + 2y^3</a>, Acta Mathematica 186 (2001), pp. 1-84.
%H A219726 Wikipedia, <a href="https://en.wikipedia.org/wiki/Roger_Heath-Brown">Roger Heath-Brown</a>
%t A219726 m = 10^3; Union[Flatten@Table[x^3 + 2 y^3, {x, m^(1/3)}, {y, ((m - x^3)/2)^(1/3)}]]
%o A219726 (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
%o A219726 (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
%Y A219726 Cf. A173587, A219722, A219725.
%K A219726 nonn
%O A219726 1,1
%A A219726 _Zak Seidov_, Nov 26 2012