A268210 Primes p of the form 2^k + 1 such that p - k is a prime q (for k >= 0).

2, 3, 5, 17, 65537

Offset: 1

Author

Jaroslav Krizek, Jan 28 2016

Keywords

• nonn

Comments

Intersection of A092506 and A268209.

Sequence is not the same as A004249 because A004249(5) is a composite number.

Corresponding values of numbers k: 0, 1, 2, 4, 16; corresponding values of primes q: 2, 2, 3, 13, 65521.

4 out of 5 known Fermat primes from A019434 (3, 5, 17, 65537) are terms.

Examples

			Prime 17 = 2^4 + 1 is a term because 17 - 4 = 13 (prime).
257 = 2^8 + 1 is not a term because 257 - 8 = 249 (composite number).
		

Crossrefs

Cf. A004249, A019434, A092506, A100361, A100362, A268209.

Programs

Magma

[2^k + 1: k in [0..60] | IsPrime(2^k + 1) and IsPrime(2^k - k + 1)];

Mathematica

2^# + 1 &@ Select[Range[0, 600], PrimeQ[2^# + 1] && PrimeQ[2^# - # + 1] &] (* Michael De Vlieger, Jan 29 2016 *)