A237360 Numbers n of the form p^2+p+1 (for prime p) such that n^2+n+1 is also prime.

57, 381, 993, 4557, 16257, 32943, 49953, 58323, 109893, 135057, 167691, 214833, 237657, 453603, 503391, 564753, 658533, 678153, 780573, 995007, 1248807, 1516593, 1746363, 2218611, 2400951, 3465183, 3738423, 4340973, 4750221, 5232657, 6118203

Offset: 1

Author

Derek Orr, Feb 06 2014

Keywords

• nonn

Examples

			57 = 7^2+7+1 (7 is prime) and 57^2+57+1 = 3307 is also prime. Thus, 57 is a member of this sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A060800, A002383.

Programs

Maple

for k from 1 do
    p := ithprime(k) ;
    n := numtheory[cyclotomic](3,p) ;
    pn := numtheory[cyclotomic](3,n) ;
    if isprime( pn) then
        print(n) ;
    end if;
end do: # R. J. Mathar, Feb 07 2014

Mathematica

Select[Table[p^2+p+1,{p,Prime[Range[500]]}],PrimeQ[#^2+#+1]&] (* Harvey P. Dale, Feb 09 2014 *)

PARI

s=[]; forprime(p=2, 4000, if(isprime(p^4+2*p^3+4*p^2+3*p+3), s=concat(s, p^2+p+1))); s \\ Colin Barker, Feb 07 2014

Python

import sympy
from sympy import isprime
{print(n**2+n+1) for n in range(10**4) if isprime(n) and isprime((n**2+n+1)**2+(n**2+n+1)+1)}