A116886 Primes p that remain prime through at least 2 iterations of the function f(p) = p^2 + 4.

3, 17, 103, 137, 277, 313, 677, 743, 1117, 1627, 2003, 2143, 3407, 3677, 4483, 5087, 5903, 7177, 7333, 8087, 8093, 8147, 8537, 8573, 9293, 9473, 10177, 10477, 11173, 13807, 14897, 15107, 16657, 19753, 21563, 22307, 24113, 26113, 26417, 26633

Offset: 1

Author

Giovanni Resta, Feb 27 2006

Keywords

• nonn

Comments

Numbers p with the property that p, q = p^2 + 4, and r = q^2 + 4 are all prime. - Zak Seidov, Sep 08 2009

a(n) = sqrt(A165218(n) - 4). - Zak Seidov, Sep 08 2009

Examples

			17 is prime, 17^2 + 4 = 293 is prime and 293^2 + 4 = 85853 is prime.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A062324, A116887, A116888, A116889, A045637, A062324, A165218.

Programs

Mathematica

Select[Prime[Range[2*7! ]],PrimeQ[ #^2+4]&&PrimeQ[(#^2+4)^2+4]&] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2010 *)
fQ[n_]:=AllTrue[Rest[NestList[#^2+4&,n,2]],PrimeQ]; Select[Prime[ Range[ 3000]],fQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 21 2014 *)

PARI

is(n)=my(q);isprime(p) && isprime(q=p^2+4) && isprime(q^2+4) \\ Charles R Greathouse IV, Nov 06 2013

Extensions

Edited by N. J. A. Sloane, Sep 18 2009 at the suggestion of R. J. Mathar