OFFSET
0,3
COMMENTS
Conjecture: The number 4 is the only perfect power in this sequence. In other words, it is impossible to have a(n) = x^m for some integers n > 3, m > 1 and x > 1. - Zhi-Wei Sun, Sep 30 2015
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.
FORMULA
a(n) = A060967(2n). - R. J. Mathar, Sep 15 2012
EXAMPLE
pi(2^3)=4 since first 4 primes are 2,3,5,7 all <= 2^3 = 8.
MATHEMATICA
Table[PrimePi[2^n], {n, 0, 46}] (* Robert G. Wilson v *)
PROG
(PARI) a(n) = primepi(1<<n); \\ John W. Nicholson, May 16 2011
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
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
STATUS
approved