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A007053
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Number of primes <= 2^n.
(Formerly M1018)
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61
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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).
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n=0..77 (from the web page of Tomas Oliveira e Silva) [a(76) and a(77) from Jens Franke et al., Jul 29 2010]
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers
Tomas Oliveira e Silva, Tables of values of pi(x) and of pi2(x)
Tomas Oliveira e Silva, Computing pi(x): the combinatorial method, REVISTA DO DETUA, VOL. 4, N 6, MARCH 2006.
Index entries for sequences related to numbers of primes in various ranges
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EXAMPLE
| pi(2^3)=4 since first 4 primes are 2,3,5,7 all <=2^3=8.
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MATHEMATICA
| Table[PrimePi[2^n], {n, 0, 46}] (* Robert G. Wilson v *)
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PROG
| (Pari) a(n) = primepi(1<<n); [John W. Nicholson, May 16 2011]
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CROSSREFS
| Cf. A006880, A036378.
Sequence in context: A131298 A168445 A185192 * A005684 A018167 A140443
Adjacent sequences: A007050 A007051 A007052 * A007054 A007055 A007056
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com), S. W. Golomb
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EXTENSIONS
| More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
Extended to n = 52 by Warren D. Smith (wds(AT)research.NJ.NEC.COM), Dec 11 2000, computed with Meissel-Lehmer-Legendre inclusion exclusion formula code he wrote back in 1985, recently re-run.
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