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A237360
Numbers n of the form p^2+p+1 (for prime p) such that n^2+n+1 is also prime.
3
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
1,1
LINKS
EXAMPLE
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.
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 *)
PROG
(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)}
(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
CROSSREFS
Sequence in context: A209517 A097200 A211147 * A076459 A268260 A184224
KEYWORD
nonn
AUTHOR
Derek Orr, Feb 06 2014
STATUS
approved