A269834 Primes p of the form 2^k + 9*(-1)^k - 8.

2, 5, 17, 257, 65537

Offset: 1

Author

Jaroslav Krizek, Mar 06 2016

Keywords

• nonn

Comments

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

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.

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.

Corresponding values of k: 0, 2, 4, 8, 16, ...

Crossrefs

Sequence is different from A132198 and A111635.

Cf. A003627, A019434.

Programs

Magma

[2^n + 9*(-1)^n - 8: n in [0..1000] | IsPrime(2^n + 9*(-1)^n - 8)];