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Primes p of the form 2^k + 9*(-1)^k - 8.
0

%I #19 Sep 13 2024 15:58:54

%S 2,5,17,257,65537

%N Primes p of the form 2^k + 9*(-1)^k - 8.

%C Union of number 2 and Fermat primes > 3 from A019434; for odd k, the numbers 2^k - 17 are divisible by 3.

%C Also primes p of the form 2^k + 12*(-1)^k - 11 for k >= 0 because for odd k, the numbers 2^k - 23 are divisible by 3.

%C Also primes p of the form 2^k + 1/2*(q + 1)*(-1)^k - 1/2*(q - 1) for k >= 0 where q = prime of the form 3m - 1 > 29 from A003627 because for odd k, the numbers 2^k - q are divisible by 3.

%C Corresponding values of k: 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