A050247 a(n) is the sum of the first A045345(n) primes.

2, 874, 5830, 2615298, 712377380, 86810649294, 794712005370, 105784534314378, 92542301212047102, 82704567079549985700, 24733255676526572596026, 3612032130800990065125528, 8102184022428756416738378

Offset

1,1

Comments

a(10) and a(11) were found by Giovanni Resta (Nov 15 2004). He states that there are no other terms for primes p < 4011201392413. See link to Prime Puzzles, Puzzle 31 below.

a(13) > 6640510710493148698166596 (sum of first pi(2*10^13) primes). - Donovan Johnson, Aug 23 2010

a(16) > 416714769731839517991408161209 (sum of first pi(1.55*10^14) primes). - Bruce Garner, Mar 06 2021

a(17) > 814043439429001245436559390420866 (sum of first 6500000004150767 primes). - Paul W. Dyson, Sep 27 2022

Links

Paul W. Dyson, Table of n, a(n) for n = 1..16 (terms 1..15 from Bruce Garner).

OEIS Wiki, Sums of powers of primes divisibility sequences

Carlos Rivera, Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k, The Prime Puzzles & Problems Connection.

Eric Weisstein's World of Mathematics, Prime Sums

Formula

a(n) = Sum_{i=1..A045345(n)} A000040(i). - R. J. Mathar, Jan 26 2008

Mathematica

A007504 = Cases[Import["https://oeis.org/A007504/b007504.txt", "Table"], {_, _}][[All, 2]];
A045345 = Cases[Import["https://oeis.org/A045345/b045345.txt", "Table"], {_, _}][[All, 2]];
Table[A007504[[A045345[[n]] + 1]], {n, 1, 5}](* Robert Price, Mar 13 2020 *)

Prog

(PARI) s=n=0; forprime(p=2, 1e9, if((s+=p)%n++==0, print1(s", "))) \\ Charles R Greathouse IV, Nov 07 2014

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248, A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Sequence in context: A199947 A230569 A239149 * A159705 A229678 A261528

Adjacent sequences: A050244 A050245 A050246 * A050248 A050249 A050250

Keyword

nonn,more

Author

Eric W. Weisstein

Extensions

a(10)-a(11) from Giovanni Resta submitted by Ray Chandler, Jul 19 2010

a(12) from Donovan Johnson, Aug 23 2010

a(13) from Robert Price, Mar 17 2013

Status

approved