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A144953 Primes of form n^3 + 2. 16
2, 3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271, 9129331, 9938377, 10503461, 12326393, 14348909, 14706127, 15438251, 18191449 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio Numerorum' III: On the expression of a number as a sum of primes, Acta Mathematica 44 (1923), 1-70.

LINKS

Vincenzo Librandi and Robert Israel, Table of n, a(n) for n = 1..10000 (first 2900 terms from Vincenzo Librandi)

FORMULA

a(n) = A067200(n)^3 + 2. - Zak Seidov, Sep 16 2013

MAPLE

N:= 10000: # number of terms desired

R[1]:= 2: count:= 1:

for n from 1 by 2 while count < N do

   p:= n^3+2;

   if isprime(p) then

     count:= count+1;

     R[count]:= p;

   end if

end do:

seq(R[n], n=1..N); # Robert Israel, Jan 29 2013

MATHEMATICA

lst={}; Do[s=n^3; If[PrimeQ[p=s+2], AppendTo[lst, p]], {n, 6!}]; lst

A144953={2}; Do[If[PrimeQ[p=n^3+2], AppendTo[A144953, p]], {n, 1, 10^5, 2}]; A144953 (* Zak Seidov, Nov 05 2008 *)

Select[Table[n^3+2, {n, 0, 7000}], PrimeQ] (* Vincenzo Librandi, Nov 30 2011 *)

PROG

(PARI) for(n=0, 1e3, if(isprime(k=n^3+2), print1(k", "))) \\ Charles R Greathouse IV, Jul 06 2010

(MAGMA) [a: n in [0..800] | IsPrime(a) where a is n^3+2]; // Vincenzo Librandi, Nov 30 2011

CROSSREFS

Cf. A067200.

Sequence in context: A116325 A228021 A053998 * A132282 A064893 A141514

Adjacent sequences:  A144950 A144951 A144952 * A144954 A144955 A144956

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Sep 26 2008

EXTENSIONS

a(1)=2 from Zak Seidov, Nov 05 2008

Reference and index correction from Charles R Greathouse IV, Jul 06 2010

STATUS

approved

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Last modified February 19 22:04 EST 2018. Contains 299357 sequences. (Running on oeis4.)