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%I #33 Sep 08 2022 08:46:19
%S 0,2,3,4,5,17,29,31,53,59,101,277,647,1061,2381,2833,3613,3853,3929,
%T 5297,7417,90217,122219,173191,256199,336353,485977,591827,1059503
%N Numbers k such that 3^k + (-2)^k is prime.
%C Numbers j such that both 3^j + (-2)^j and 3^j + (-4)^j are primes: 0, 3, 4, 17, 59, ...
%C See Michael Somos comment in A082101.
%C Probably this is just A057468 with 0,2,4 added, because we already know that if another even number belong to this sequence it must be greater than log_3(10^16000000) = about 3.3*10^7. This is because 3^n+2^n can be a prime with n>0 only if n is a power of 2. - _Giovanni Resta_, Mar 12 2017
%e 4 is in this sequence because 3^4 + (-2)^4 = 97 is prime.
%t Select[Range[0, 10000], PrimeQ[3^# + (-2)^#] &] (* _G. C. Greubel_, Jul 29 2018 *)
%o (Magma) [n: n in [0..1000] | IsPrime(3^n+(-2)^n)];
%o (PARI) is(n)=isprime(3^n+(-2)^n) \\ _Charles R Greathouse IV_, Mar 16 2017
%Y Cf. A174326. Subsequence of A087451. Supersequence of A057468.
%Y Cf. A082101.
%K nonn,more
%O 1,2
%A _Juri-Stepan Gerasimov_, Mar 12 2017