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%I #7 Sep 08 2022 08:46:16
%S 2,5,17,257,65537
%N Primes p of the form 2^n + 9*(-1)^n - 8.
%C Union of number 2 and Fermat primes > 3 from A019434; for odd n, numbers 2^n - 17 are divisible by 3.
%C Also primes p of the form 2^n + 12*(-1)^n - 11 for n >= 0 because for odd n, numbers 2^n - 23 are divisible by 3.
%C Also primes p of the form 2^n + 1/2*(q + 1)*(-1)^n - 1/2*(q - 1) for n >= 0 where q = prime of the form 3m - 1 > 29 from A003627 because for odd n, numbers 2^n - q are divisible by 3.
%C Corresponding values of n: 0, 2, 4, 8, 16, ...
%o (Magma) [2^n + 9*(-1)^n - 8: n in [0..1000] | IsPrime(2^n + 9*(-1)^n - 8)]
%Y Sequence is different from A132198 and A111635.
%Y Cf. A003627, A019434.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Mar 06 2016
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