A086680 Number of primes < 4^n.

0, 2, 6, 18, 54, 172, 564, 1900, 6542, 23000, 82025, 295947, 1077871, 3957809, 14630843, 54400028, 203280221, 762939111, 2874398515, 10866266172, 41203088796, 156661034233, 597116381732, 2280998753949, 8731188863470, 33483379603407, 128625503610475, 494890204904784

Offset

0,2

Comments

These numbers approximate the sum of primes < 2^n. The sum of primes < 2^20 = A130739(20) = 41162256126. The number of primes < 2^40 = 41203088796. The error is -0.000991993. From A007053, we have number of primes < 2^74 = 375744164937699609596 and sum of primes < 2^37 = 375743480734175191581 for an error of -0.0000018209325.

Links

Amiram Eldar, Table of n, a(n) for n = 0..46 (calculated from the b-file at A007053)

Cino Hilliard, Sum of primes less than n [Dead link]

Formula

a(n) = A007053(2*n). - Amiram Eldar, Jun 06 2024

Example

a(2) = 6 because there are 6 primes, 2, 3, 5, 7, 11, and 13 that are < 4^2.

Crossrefs

Cf. A007053, A130739.

Sequence in context: A007206 A062415 A363432 * A275872 A148455 A094590

Adjacent sequences: A086677 A086678 A086679 * A086681 A086682 A086683

Keyword

nonn

Author

Cino Hilliard, Jul 28 2003

Extensions

Extended by Cino Hilliard, Feb 13 2009

a(25)-a(27) from Amiram Eldar, Jun 06 2024

Status

approved