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A173587
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Primes of the form x^3 + 2y^3, with x,y >0.
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12
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3, 17, 29, 43, 127, 179, 251, 277, 359, 397, 433, 557, 593, 811, 857, 1051, 1367, 1459, 1583, 1753, 1801, 2017, 2027, 2213, 2251, 2447, 2663, 2689, 2729, 2789, 3221, 3331, 3391, 3457, 3581, 4421, 4519, 4787, 4967, 5653, 6037, 6217, 7109, 7883, 8081
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OFFSET
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1,1
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COMMENTS
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Heath-Brown shows that this sequence is infinite.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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