A052435 - OEIS

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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.

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: A225180 A063982 A055020 * A094701 A210452 A209312` `Adjacent sequences: A052432 A052433 A052434 * A052436 A052437 A052438`
	KEYWORD	`sign,changed`
	AUTHOR	`Eric W. Weisstein`
	STATUS	`approved`

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Last modified May 22 14:27 EDT 2013. Contains 225551 sequences.