A139390 Sum of primes <= 3^n.

0, 5, 17, 100, 791, 5830, 42468, 327198, 2575838, 20476640, 166554645, 1353822880, 11150031169, 92258920888, 769310640408, 6447635236133, 54292816788848, 459112338326268, 3896226837717653, 33172345145637461, 283258796052356059, 2425130743589880412, 20812174068479995267

Offset: 0

Author

Cino Hilliard, Jun 09 2008

Keywords

• nonn

Comments

For large n, these numbers can be closely approximated by the number of primes < (3^n)^2. For example, the sum of primes < 3^12 = 11150031169. The number of primes < (3^12)^2 = 3^24 = 11152818693. The error here 0.000250.

The second term, 5, is the addition of the primes 2 and 3 since we defined the sequence as less than or equal.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..43 (calculated using Kim Walisch's primesum program)
• Cino Hilliard, Sum of Primes. [broken link]
• Cino Hilliard, Sumprimesgmp program. [broken link]
• Kim Walisch, Sum of the primes below x (primesum).

Crossrefs

Cf. A000244, A034387, A130739.

Programs

PARI

a(n) = vecsum(primes([1, 3^n])); \\ Michel Marcus, Jul 02 2024

Formula

a(n) = A034387(A000244(n)). - Amiram Eldar, Jul 02 2024

Extensions

Duplicated term removed and a(20)-a(22) added by Amiram Eldar, Jul 02 2024