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%I #12 Jan 19 2019 04:14:59
%S 3,5,7,13,43,89,313,613,643,743,1171,1279,1627,1823,1867,1999,2311,
%T 2393,2683,2753,2789,3571,4441,4561,5039,5231,5647,5953,6067,6317,
%U 6899,8039,8087,8753,8923,9337,9787,9931,10259,10667
%N Primes p with prime(p) + 2 and prime(p) + 6 both prime.
%C According to the conjecture in A236472, this sequence contains infinitely many terms, i.e., there are infinitely many prime triples of the form {prime(p), prime(p) + 2, prime(p) + 6} with p prime.
%C See A236462 for a similar sequence.
%H Zhi-Wei Sun, <a href="/A236464/b236464.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 3 since 3, prime(3) + 2 = 7 and prime(3) + 6 = 11 are all prime, but prime(2) + 6 = 9 is composite.
%t p[n_]:=p[n]=PrimeQ[Prime[n]+2]&&PrimeQ[Prime[n]+6]
%t n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10000}]
%Y Cf. A000040, A022004, A236457, A236458, A236462, A236472.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 26 2014