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%I #36 Sep 11 2024 14:42:12
%S 2,3,43,61,5563,10093
%N Primes p such that 3^p - 2^p - 2 is also prime.
%C The associated 3^p-2^p-2 are in A162713.
%C The list of k such that 3^k-2^k-2 is prime is: 2, 3, 43, 61, 63, 1369, ..., where 63 and 1369 are not prime.
%C No other term <= 15000. - _Emeric Deutsch_, Aug 03 2009
%C a(7) > 25000. - _Tyler NeSmith_, Jul 10 2021
%C a(7) > 2*10^5. - _Michael S. Branicky_, Sep 11 2024
%e 2 is in the sequence because 3^2-2^2-2 = 3 is prime.
%e 3 is in the sequence because 3^3-2^3-2 = 17 is prime.
%p a := proc(n) if isprime(n) and isprime(3^n-2^n-2) then n end if end proc:
%p seq(a(n), n = 1 .. 15000); # _Emeric Deutsch_, Aug 03 2009
%t Select[Prime[Range[11000]], PrimeQ[3^# - 2^# - 2] &] (* _Vincenzo Librandi_, Sep 25 2015 *)
%o (PARI) forprime(p=2, 1e3, if (isprime(3^p-2^p-2), print1(p, ", "))) \\ _Altug Alkan_, Sep 25 2015
%o (Magma) [p: p in PrimesUpTo(1000) | IsPrime(3^p-2^p-2)];// _Vincenzo Librandi_, Sep 26 2015
%Y Cf. A162713.
%K nonn,more
%O 1,1
%A _Vincenzo Librandi_, Jul 11 2009
%E Edited by _R. J. Mathar_, Jul 26 2009
%E a(5)-a(6) from _Emeric Deutsch_, Aug 03 2009