A052435 a(n) = round(li(n) - pi(n)), where li is the logarithmic integral and pi(x) is the number of primes <= x.

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

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

Chris K. 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
(SageMath) [round(li(n) - prime_pi(n)) for n in (2..105)] # G. C. Greubel, May 17 2019

Crossrefs

Cf. A000720, A052434, A282870, A359145.

Sequence in context: A327160 A355832 A055020 * A094701 A210452 A347037

Adjacent sequences: A052432 A052433 A052434 * A052436 A052437 A052438

Keyword

sign,look

Author

Eric W. Weisstein

Status

approved