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%I #10 Feb 13 2024 18:30:56
%S 3,5,11,31,41,43,47,67,79,107,199,223,251,263,311,313,461,467,499,577,
%T 599,641,727,743,797,911,919,929,1163,1187,1277,1303,1429,1433,1447,
%U 1613,1619,1621,1637,1783,1789,1823,1831,1867,1879,1997,2029,2039,2089,2309
%N Primes p with prime(p + 2) + 2 prime.
%C This sequence is interesting because of the conjecture in A236566.
%C Note that A236457 is a subsequence of the sequence.
%H Zhi-Wei Sun, <a href="/A236568/b236568.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 3 since prime(3 + 2) + 2 = 11 + 2 = 13 is prime, but prime (2 + 2) + 2 = 9 is not.
%t p[n_]:=PrimeQ[Prime[n+2]+2]
%t n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10000}]
%t Select[Prime[Range[400]],PrimeQ[Prime[#+2]+2]&] (* _Harvey P. Dale_, Feb 13 2024 *)
%Y Cf. A000040, A001359, A006512, A236457, A236566.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 28 2014