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%I #16 Jan 20 2015 02:21:44
%S 3,17,103,137,277,313,677,743,1117,1627,2003,2143,3407,3677,4483,5087,
%T 5903,7177,7333,8087,8093,8147,8537,8573,9293,9473,10177,10477,11173,
%U 13807,14897,15107,16657,19753,21563,22307,24113,26113,26417,26633
%N Primes p that remain prime through at least 2 iterations of the function f(p) = p^2 + 4.
%C Numbers p with the property that p, q = p^2 + 4, and r = q^2 + 4 are all prime. - _Zak Seidov_, Sep 08 2009
%C a(n) = sqrt(A165218(n) - 4). - _Zak Seidov_, Sep 08 2009
%H Zak Seidov, <a href="/A116886/b116886.txt">Table of n, a(n) for n = 1..1000</a>
%e 17 is prime, 17^2 + 4 = 293 is prime and 293^2 + 4 = 85853 is prime.
%t Select[Prime[Range[2*7! ]],PrimeQ[ #^2+4]&&PrimeQ[(#^2+4)^2+4]&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2010 *)
%t 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 *)
%o (PARI) is(n)=my(q);isprime(p) && isprime(q=p^2+4) && isprime(q^2+4) \\ _Charles R Greathouse IV_, Nov 06 2013
%Y Cf. A062324, A116887, A116888, A116889, A045637, A062324, A165218.
%K nonn
%O 1,1
%A _Giovanni Resta_, Feb 27 2006
%E Edited by _N. J. A. Sloane_, Sep 18 2009 at the suggestion of _R. J. Mathar_
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