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Consider primes p and q such that p = 3^k + 2 and q = 3^(k+1) + 2 for some k; sequence gives values of p.
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%I #16 Jul 07 2024 03:19:51

%S 3,5,11,29,4782971

%N Consider primes p and q such that p = 3^k + 2 and q = 3^(k+1) + 2 for some k; sequence gives values of p.

%C a(6) > 3^1400000 + 2, if it exists (cf. A051783). - _Amiram Eldar_, Jul 07 2024

%e 3^1 + 2 = 5, 3^2 + 2 = 11.

%t 3^#+2&/@Select[Range[0,20],AllTrue[{3^#+2,3^(#+1)+2},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Nov 01 2015 *)

%o (PARI) g(m,n,b) = { for(x=0,n, y=m+b^x+b%2; z=m+b^(x+1)+b%2; if(isprime(y)&isprime(z),print1(p",") ) ) }

%Y Cf. A051783.

%K nonn

%O 1,1

%A _Cino Hilliard_, Jun 29 2005

%E Offset corrected by _Amiram Eldar_, Jul 07 2024