OFFSET
1,1
COMMENTS
Heath-Brown shows that this sequence is infinite.
LINKS
Zak Seidov, Table of n, a(n) for n = 1..1000
D. R. Heath-Brown, Primes represented by x^3 + 2y^3, Acta Mathematica 186 (2001), pp. 1-84.
H. Iwaniec, Primes represented by quadratic polynomials in two variables, Acta Arithmetica, 24 (1974), 435-459
T. Mitsui, Generalized prime number theorem, Jap.J. Math,26 (1956),1-42
EXAMPLE
a(1) = 1^3+2*1^3 =3, prime. a(2) = 1^3 + 2* 2^3 = 17. a(7) = 1^3+2*r^3 =251.
MAPLE
T:=array(0..5000000): ind:=1: for x from 1 to 1000 do: for y from 1 to 1000 do: z:=x^3 + 2*y^3: if type(z, prime)=true then T[ind] :=z: ind :=ind+1: else fi: od: od: mini:=T[1]: ii:=1: for p from 1 to ind-1 do: for n from 1 to ind-1 do: if T[n] < mini then mini:= T[n]: ii:=n: else fi: od: print(mini): T[ii]:= 999999999999999: ii:=1: mini:=T[1] : od:
MATHEMATICA
formQ[p_] := Reduce[0 < x < p^(1/3) && 0 < y < (p/2)^(1/3) && x^3 + 2 y^3 == p, {x, y}, Integers] =!= False; Select[ Prime[ Range[1100]], formQ] (* Jean-François Alcover, Sep 28 2011 *)
PROG
(PARI) list(lim)=my(v=List(), t); for(y=1, sqrtn(lim\2, 3), t=2*y^3; for(x=1, sqrtn(lim-t, 3), if(isprime(t+x^3), listput(v, t+x^3)))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Sep 28 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 22 2010
EXTENSIONS
Converted references to links - R. J. Mathar, Feb 24 2010
STATUS
approved