A099825 Sum of the first 2^n primes.

2, 5, 17, 77, 381, 1851, 8893, 41741, 191755, 868151, 3875933, 17120309, 74950547, 325590115, 1405167561, 6029676711, 25750781177, 109495928099, 463852117169, 1958476902435, 8244703036797, 34615624751259, 144991244981985

Offset

0,1

Links

Amiram Eldar, Table of n, a(n) for n = 0..65 (calculated using Kim Walisch's primesum program; terms 0..30 from Robert G. Wilson v)

Cino Hilliard, Sumprimes. [broken link]

Kim Walisch, Sum of the primes below x (primesum).

Formula

a(n) = A007504(A000079(n)). - Amiram Eldar, Jul 01 2024

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[0] = 2; f[n_] := f[n] = Block[{k = 0, mx = 2^n/2, np = Prime[2^n/2], s = f[n - 1]}, While[k < mx, k++; np = NextPrim@np; s = s + np]; s]; Table[ f@n, {n, 0, 23)] (* Robert G. Wilson v, Aug 24 2006 *)
Module[{nn=22, ap}, ap=Accumulate[Prime[Range[2^nn]]]; Table[ap[[2^n]], {n, 0, nn}]] (* Harvey P. Dale, Apr 12 2017 *)

Prog

(PARI) a(n)=my(s); forprime(p=2, , s+=p; if(n--==0, return(s))) \\ Charles R Greathouse IV, Feb 16 2017

Crossrefs

Cf. A000040, A000079, A006988, A007504, A033844, A099824, A099826, A121248.

Sequence in context: A328504 A375631 A279208 * A014288 A330046 A343848

Adjacent sequences: A099822 A099823 A099824 * A099826 A099827 A099828

Keyword

nonn

Author

Robert G. Wilson v, Oct 25 2004

Status

approved