A268209 Numbers n of the form 2^k + 1 such that n - k is a prime q (for k >= 0).

2, 3, 5, 17, 65, 65537, 262145, 18014398509481985, 288230376151711745, 1267650600228229401496703205377, 1329227995784915872903807060280344577

Offset: 1

Author

Jaroslav Krizek, Jan 28 2016

Keywords

• nonn

Comments

Subsequence of A000051.

Prime terms are in A268210: 2, 3, 5, 17, 65537, ...

Corresponding values of numbers k are in A100361 (numbers n such that 2^n-n+1 is prime).

Corresponding values of primes q are in A100362 (primes of the form 2^n-n+1).

4 out of 5 known Fermat primes (3, 5, 17, 65537) are terms; corresponding values of primes q: 2, 3, 13, 65521.

Examples

			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).
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..12

Crossrefs

Cf. A100361, A100362, A268210, A268211.

Programs

Magma

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

Mathematica

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

Formula

a(n) = A100362(n) + A100361(n).