%I #8 Oct 11 2020 18:47:20
%S 3,11,29,149,179,191,269,347,431,461,617,659,1031,1619,1931,3467,3527,
%T 4799,6569,6689,7349,7877,9011,9767,11117,12611,13691,13901,14549,
%U 16067,16139,16451,16631,17489,17681,18911,20981,22367,23909,24179
%N Primes p with p + 2 and prime(p) - 2 both prime.
%C According to the conjecture in A236468, this sequence should have infinitely many terms.
%C See A236457 and A236458 for similar sequences.
%H Zhi-Wei Sun, <a href="/A236467/b236467.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 3 since 3, 3 + 2 = 5 and prime(3) - 2 = 3 are all prime, but 2 + 2 = 4 is composite.
%t p[n_]:=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}]
%t Select[Prime[Range[3000]],AllTrue[{#+2,Prime[#]-2},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 11 2020 *)
%Y Cf. A000040, A001359, A006512, A236119, A236457, A236458, A236462, A236464, A236468.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 26 2014