0,2

Number of primes with at most n digits; or pi(10^n).

Also omega( (10^n)! ), where omega(x): number of distinct prime divisors of x. - Cino Hilliard (hillcino368(AT)hotmail.com), Jul 04 2007

This sequence also gives a good approximation for the sum of primes < 10^(n/2). This is evident from the fact that the number of primes < 10^2n closely approximates the sum of primes < 10^n. See link on Sum of Primes for the derivation. - Cino Hilliard (hillcino368(AT)hotmail.com), Jun 08 2008

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 11.

A. Granville and G. Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.

C. T. Long, Elementary Introduction to Number Theory. Prentice-Hall, Englewood Cliffs, NJ, 1987, p. 77.

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 179.

H. Riesel, "Prime numbers and computer methods for factorization," Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, page 38.

M. du Sautoy, The Music of the Primes, Fourth Estate / HarperCollins, 2003; see p. 48.

D. Shanks, Solved and Unsolved Problems in Number Theory. Chelsea, NY, 2nd edition, 1978, p. 15.

N. J. A. Sloane, Table of n, a(n) for n=0..23 (from the web page of Tomas Oliveira e Silva)

C. K. Caldwell, How Many Primes Are There?

C. K. Caldwell, Mark Deleglise's work

Xavier Gourdon, a(22) found by pi(x) project

Xavier Gourdon & Pascal Sebah, The pi(x) project : results and current computations

A. Granville and G. Martin, Prime number races

R. K. Hoeflin, Titan Test

J. C. Lagarias, V. S. Miller, and A. M. Odlyzko, Computing pi(x): The Meissel-Lehmer method, Math. Comp., 44 (1985), pp. 537-560.

J. C. Lagarias and A. M. Odlyzko, Computing pi(x): An analytic method, J. Algorithms, 8 (1987), pp. 173-191.

Tomas Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

M. R. Watkins, The distribution of prime numbers

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Wikipedia, Prime number theorem

Index entries for sequences related to numbers of primes in various ranges

Cino Hilliard, Sum of primes

Partial sums of A006879. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 25 2004

Table[PrimePi[10^n], {n, 0, 16}]

(PARI) g(n) = for(x=0, n, print1(omega((10^x)!), ", ")) - Cino Hilliard (hillcino368(AT)hotmail.com), Jul 04 2007

Cf. A000720, A006879, A007053, A040014, A006988.

Sequence in context: A073517 A074422 A128419 this_sequence A081068 A140177 A034494

Adjacent sequences: A006877 A006878 A006879 this_sequence A006881 A006882 A006883

nonn,base,hard,nice

njas, Simon Plouffe (plouffe(AT)math.uqam.ca)

Lehmer gave the incorrect value 455052512 for the 10th term. More terms 5/96. Jud McCranie (j.mccranie(AT)comcast.net) points out that the 11-th term is not 4188054813 but rather 4118054813.

a(22) from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 04 2001

a(23) (see Gourdon and Sebah) has yet to be verified and the assumed error is +/-1. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 10 2002. The actual error was 14037804. - njas, Nov 28 2007

a(23) corrected by njas from the web page of Tomas Oliveira e Silva, Nov 28 2007