A007053 Number of primes <= 2^n.
0, 1, 2, 4, 6, 11, 18, 31, 54, 97, 172, 309, 564, 1028, 1900, 3512, 6542, 12251, 23000, 43390, 82025, 155611, 295947, 564163, 1077871, 2063689, 3957809, 7603553, 14630843, 28192750, 54400028, 105097565, 203280221, 393615806, 762939111, 1480206279, 2874398515, 5586502348, 10866266172, 21151907950, 41203088796, 80316571436, 156661034233, 305761713237, 597116381732, 1166746786182, 2280998753949, 4461632979717, 8731188863470, 17094432576778, 33483379603407, 65612899915304, 128625503610475
Offset: 0
Examples
pi(2^3)=4 since first 4 primes are 2,3,5,7 all <= 2^3 = 8.
References
- Jens Franke et al., pi(10^24), Posting to the Number Theory Mailing List, Jul 29 2010.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- David Baugh, Table of n, a(n) for n = 0..92 (terms n = 87..92 found using Kim Walisch's primecount program, terms n = 0..86 from Charles R Greathouse IV and Douglas B. Staple, [a(0)-a(75) from Tomás Oliveira e Silva, a(76)-a(77) from Jens Franke et al., Jul 29 2010, a(78)-a(80) from Jens Franke et al. on the Riemann Hypothesis, verified unconditionally by Douglas B. Staple, and a(81)-a(86) from Douglas B. Staple])
- Andrew R. Booker, The Nth Prime Page
- S. W. Golomb, Letter to N. J. A. Sloane, Jul. 1991
- Thomas R. Nicely, Some Results of Computational Research in Prime Numbers
- Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [Local copy, pdf only]
- Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)
- Tomás Oliveira e Silva, Computing pi(x): the combinatorial method, Revista Do Detua, Vol. 4, No 6, March 2006.
- Douglas B. Staple, The combinatorial algorithm for computing pi(x), arXiv:1503.01839 [math.NT], 2015.
- Index entries for sequences related to numbers of primes in various ranges
Programs
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Mathematica
Table[PrimePi[2^n], {n, 0, 46}] (* Robert G. Wilson v *) -
PARI
a(n) = primepi(1<
Formula
a(n) = A060967(2n). - R. J. Mathar, Sep 15 2012
Extensions
More terms from Jud McCranie
Extended to n = 52 by Warren D. Smith, Dec 11 2000, computed with Meissel-Lehmer-Legendre inclusion exclusion formula code he wrote back in 1985, recently re-run.
Extended to n = 86 by Douglas B. Staple, Dec 18 2014
Comments