%I #14 Sep 08 2022 08:46:15

%S 2,5,65,

%T 110427941548649020598956093796432407239217743554726184882600387580788737

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

%C Subsequence of A000051.

%C Corresponding values of numbers k are in A100359 (numbers n such that 2^n+n+1 is prime).

%C Corresponding values of primes q are in A061421 (primes of the form 2^n+n+1).

%F a(n) = A061421(n) - A100359(n).

%e 65 = 2^6 + 1 is a term because 65 + 6 = 71 (prime).

%t 2^# + 1 &@ Select[Range[0, 600], PrimeQ[2^# + # + 1] &] (* _Michael De Vlieger_, Jan 29 2016 *)

%o (Magma) [2^n + 1: n in [0..600] | IsPrime(2^n + n + 1)]

%Y Cf. A061421, A100359, A268209.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Jan 28 2016