

A300692


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


0




OFFSET

1,1


COMMENTS

Elements in the sequence are certified primes.
The corresponding exponents of 2 are 1, 2, 3, 4, 16 and 54.


LINKS

Table of n, a(n) for n=1..6.
Kim Walish List of sums of primes up to 2^n with n<=80 (at the end).


FORMULA

Numbers of the form Sum_{i=2..2^n1} A061397(i) that are prime.


EXAMPLE

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


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A130739, A061397.
Sequence in context: A081763 A013918 A007351 * A076076 A136194 A056304
Adjacent sequences: A300689 A300690 A300691 * A300693 A300694 A300695


KEYWORD

nonn,more


AUTHOR

Christoph Zurnieden, Apr 03 2018


STATUS

approved



