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

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.

Justification sumprimes(n) ~ Pi(n^2) can be found in the link.

Links

Table of n, a(n) for n=0..24.

Cino Hilliard, Sum of primes less than n [Cino Hilliard, Feb 13 2009]

Example

for n=2, 2,3,5,7,11,13 are the 6 primes < 2^4.

Crossrefs

Cf. A007053, A130739.

Sequence in context: A114464 A007206 A062415 * 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

Status

approved