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%I #15 Apr 12 2014 13:15:24
%S 3,5,17,41,1949,2309,2711,2789,2801,3299,3329,3359,3917,4157,4217,
%T 4259,4637,5009,5021,5231,6449,7757,8087,8219,8627,9419,9929,10007,
%U 10937,11777,12071,14321,15647,15971,16061,16901,18131,18251,18287,18539
%N Primes p with p + 2 and prime(p) + 2 both prime.
%C According to the conjecture in A236470, the sequence should have infinitely many terms. This is stronger than the twin prime conjecture.
%C See A236457 and A236467 for similar sequences.
%H Zhi-Wei Sun, <a href="/A236458/b236458.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 3 since 3 + 2 = 5 and prime(3) + 2 = 7 are both prime, but 2 + 2 = 4 is composite.
%t p[n_]:=PrimeQ[n+2]&&PrimeQ[Prime[n]+2]
%t n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10000}]
%o (PARI) s=[]; forprime(p=2, 20000, if(isprime(p+2) && isprime(prime(p)+2), s=concat(s, p))); s \\ _Colin Barker_, Jan 26 2014
%Y Cf. A000040, A001359, A006512, A236119, A236456, A236457, A236467, A236470.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 26 2014
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