%I #33 Jan 28 2022 17:05:56

%S 2,5,17,41,202288087,4394533064208947008756469709307

%N Primes that are the sum of all primes up to some power of 2.

%C Elements in the sequence are certified primes.

%C The corresponding exponents of 2 are 1, 2, 3, 4, 16 and 54.

%H Kim Walisch, <a href="https://github.com/kimwalisch/primesum/blob/master/README.md">List of sums of primes up to 2^n with n<=80</a> (at the end).

%F Numbers of the form Sum_{i=2..2^n-1} A061397(i) that are prime.

%e 17 is a term because the sum of all primes below 2^3 is 2+3+5+7 = 17 which is prime.

%t Select[Array[Total@ Prime@ Range@ PrimePi[2^#] &, 27, 0], PrimeQ] (* _Michael De Vlieger_, Apr 10 2018 *)

%o (PARI) lista(nn) = {for (n=0, nn, s = 0; forprime(k=0, 2^n, s+=k); if (isprime(s), print1(s, ", ")));}

%Y Cf. A130739, A061397.

%K nonn,more

%O 1,1

%A _Christoph Zurnieden_, Apr 03 2018