

A052435


a(n) = round(li(n)  pi(n)), where li is the logarithmic integral and pi(x) is the number of primes up to x.


10



0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4
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OFFSET

2,8


COMMENTS

Eventually contains negative terms!
The logarithmic integral is the "American" version starting at 0.
The first crossover (P. Demichel) is expected to be around 1.397162914*10^316.  Daniel Forgues, Oct 29 2011


LINKS

Harry J. Smith, Table of n, a(n) for n = 2..20000
C. Caldwell, How many primes are there?
Patrick Demichel, The prime counting function and related subjects, April 05, 2005, 75 pages.
Eric Weisstein's World of Mathematics, Prime Counting Function
Eric Weisstein's World of Mathematics, Logarithmic Integral
Eric Weisstein's World of Mathematics, Skewes Number


MATHEMATICA

Table[Round[LogIntegral[x]PrimePi[x]], {x, 2, 100}]


PROG

(PARI) a(n)=round(real(eint1(log(n)))primepi(n)) \\ Charles R Greathouse IV, Oct 28 2011
(MAGMA) [Round(LogIntegral(n)  #PrimesUpTo(n)): n in [2..105]]; // G. C. Greubel, May 17 2019
(Sage) [round(li(n)  prime_pi(n)) for n in (2..105)] # G. C. Greubel, May 17 2019


CROSSREFS

Cf. A052434.
Sequence in context: A318882 A327160 A055020 * A094701 A210452 A240301
Adjacent sequences: A052432 A052433 A052434 * A052436 A052437 A052438


KEYWORD

sign,look


AUTHOR

Eric W. Weisstein


STATUS

approved



