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A052435 Round(li(n) - pi(n)), where li is the logarithmic integral and pi(x) is the number of primes up to x. 8
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 (list; graph; refs; listen; history; text; internal format)
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(-eint1(-log(n))-primepi(n)) \\ Charles R Greathouse IV, Oct 28 2011

CROSSREFS

Cf. A052434.

Sequence in context: A229895 A063982 A055020 * A094701 A210452 A240301

Adjacent sequences:  A052432 A052433 A052434 * A052436 A052437 A052438

KEYWORD

sign

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified December 22 09:10 EST 2014. Contains 252331 sequences.