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A300692 Primes that are the sum of all primes up to some power of 2. 0
2, 5, 17, 41, 202288087, 4394533064208947008756469709307 (list; graph; refs; listen; history; text; internal format)
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^n-1} 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

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Last modified October 23 22:58 EDT 2019. Contains 328379 sequences. (Running on oeis4.)