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%I #32 Sep 08 2022 08:45:38
%S 2,3,29,127,24391,91127,250049,274627,328511,357913,571789,1157627,
%T 1442899,1860869,2146691,2924209,3581579,5000213,5177719,6751271,
%U 9129331,9938377,10503461,12326393,14348909,14706127,15438251,18191449
%N Primes of form n^3 + 2.
%C The Hardy-Littlewood conjecture K (p. 51) suggests that this sequence is infinite and gives an asymptotic estimate for the density of this sequence. - _Charles R Greathouse IV_, Jul 06 2010
%H Vincenzo Librandi and Robert Israel, <a href="/A144953/b144953.txt">Table of n, a(n) for n = 1..10000</a> (first 2900 terms from Vincenzo Librandi)
%H G. H. Hardy and J. E. Littlewood, <a href="https://doi.org/10.1007/BF02403921">Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes</a>, Acta Math., Vol. 44, No. 1 (1923), pp. 1-70.
%F a(n) = A067200(n)^3 + 2. - _Zak Seidov_, Sep 16 2013
%p N:= 10000: # number of terms desired
%p R[1]:= 2: count:= 1:
%p for n from 1 by 2 while count < N do
%p p:= n^3+2;
%p if isprime(p) then
%p count:= count+1;
%p R[count]:= p;
%p end if
%p end do:
%p seq(R[n],n=1..N); # Robert Israel, Jan 29 2013
%t lst={};Do[s=n^3;If[PrimeQ[p=s+2],AppendTo[lst,p]],{n,6!}];lst
%t A144953={2};Do[If[PrimeQ[p=n^3+2],AppendTo[A144953,p]],{n,1,10^5,2}];A144953 (* _Zak Seidov_, Nov 05 2008 *)
%t Select[Table[n^3+2,{n,0,7000}],PrimeQ] (* _Vincenzo Librandi_, Nov 30 2011 *)
%o (PARI) for(n=0,1e3,if(isprime(k=n^3+2),print1(k","))) \\ _Charles R Greathouse IV_, Jul 06 2010
%o (Magma) [a: n in [0..800] | IsPrime(a) where a is n^3+2]; // _Vincenzo Librandi_, Nov 30 2011
%Y Cf. A067200.
%K nonn,easy
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 26 2008
%E a(1)=2 from _Zak Seidov_, Nov 05 2008
%E Reference and index correction from _Charles R Greathouse IV_, Jul 06 2010
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