A113634 -id:A113634 - cp's OEIS frontend

A113633 Sum of the first 5^n primes.

2, 28, 1060, 39612, 1336090, 42157238, 1271530648, 37178373556, 1062895088910, 29878892909030, 828999068943506, 22762324818835316, 619715756464336328, 16753554900339748756, 450233110894196298638, 12038074430656287496566, 320451759639384414082274, 8497567719126134980044214

Offset: 0

Cino Hilliard, Jan 15 2006

nonn

Using the program at the link, computation of the next term, a(15), would require generating a list of the first 31 * 10^9 8-byte primes (file size: 250 GB). Given runtimes of 0.06, 0.13, 0.63, 7.5, 64.6, 375.38, and 2092.56 seconds on a 2.53 GHz P4 processor for a(8) through a(14), respectively, the program in the link will sum the first 5^15 primes in 3.5 hours. [Comment reworded by Jon E. Schoenfield, Aug 01 2015]

			The first 5^1 primes add up to 28.

Amiram Eldar, Table of n, a(n) for n = 0..24 (calculated using Kim Walisch's primesum program)
Cino Hilliard, SumPrimes. [broken link]
Kim Walisch, Sum of the primes below x (primesum).

Cf. A000351, A007504, A055680, A099825, A099826, A113634, A113635.

t = {}; c = 1; k = 3; s = 2; Do[ While[c < 5^n, If[PrimeQ[k], c++; s += k]; k += 2]; Print@s; AppendTo[t, s], {n, 0, 10}]; t (* Robert G. Wilson v, Jan 17 2006 *)

a(n) = A007504(A000351(n)). - Michel Marcus, Aug 01 2015

a(15) onwards from Amiram Eldar, Jul 01 2024

A113635 Sum of the first 7^n primes.

Original entry on oeis.org

2, 58, 4888, 363288, 24047406, 1482656786, 87401659166, 4997438572618, 279544493456056, 15382405126365576, 835737977869494888, 44947274043643171988, 2397349106561086277820, 126986150948361831547964, 6687136917574958175921116, 350384258762032443770716600

Offset: 0

Cino Hilliard, Jan 15 2006

nonn

			The first 7^1 primes add up to 58.

Amiram Eldar, Table of n, a(n) for n = 0..20 (calculated using Kim Walisch's primesum program)
Kim Walisch, Sum of the primes below x (primesum).

Cf. A000420, A007504, A058239, A099825, A099826, A113633, A113634.

t = {}; c = 1; k = 3; s = 2; Do[While[c < 7^n, If[ PrimeQ@k, c++; s += k]; k += 2]; Print@s; AppendTo[t, s], {n, 0, 9}]; t (* Robert G. Wilson v, Jan 17 2006 *)
Table[Total[Prime[Range[7^n]]],{n,0,7}] (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Jan 18 2024 *)

a(n) = A007504(A000420(n)). - Michel Marcus, Aug 01 2015

a(12) onwards from Amiram Eldar, Jul 01 2024

cp's OEIS Frontend

A113633 Sum of the first 5^n primes.

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