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%I #10 Feb 21 2017 01:57:58
%S 2,3,4,5,7,8,9,11,13,17,20,23,25,31,43,47,85,101,117,173,224,277,281,
%T 349,359,365,403,521,629,691,709,819,1037
%N Numbers n such that both 2^k*3^(n-k) - 1 and 2^(n-k)*3^k - 1 are primes for some positive k < n.
%e 2 is in this sequence because 2^1*3^(2-1) - 1 = 5 is prime and 2^(2-1)*3^1 - 1 = 5 is prime.
%e 3 is in this sequence because 2^1*3^(3-1) - 1 = 17 is prime and 2^(3-1)*3^1 - 1 = 11 is prime.
%e 4 is in this sequence because 2^1*3^(4-1) - 1 = 53 is prime and 2^(4-1)*3^1 - 1 = 23 is prime.
%e 5 is in this sequence because 2^2*3^(5-2) - 1 = 107 is prime and 2^(5-2)*3^2 - 1 = 71 is prime.
%t Select[Range@ 800, Function[n, Total@ Boole@ Table[PrimeQ@ {2^k*3^(n - k) - 1 , 2^(n - k)*3^k - 1} == {True, True}, {k, n/2}] > 0]] (* _Michael De Vlieger_, Feb 07 2017 *)
%o (PARI) is(n)=for(k=1,n-1, if(isprime(3^(n-k)<<k - 1) && isprime(3^k<<(n-k) - 1), return(1))); 0 \\ _Charles R Greathouse IV_, Feb 21 2017
%K nonn,more
%O 1,1
%A _Juri-Stepan Gerasimov_, Feb 06 2017
%E More terms from _Michael De Vlieger_, Feb 07 2017
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