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

Author

Eric W. Weisstein

Keywords

• nonn
• more

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

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.

Programs

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 *)

PARI

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

Formula

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

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