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URL: https://oeis.org/A052435

⇱ A052435 - OEIS

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A052435
a(n) = round(li(n) - pi(n)), where li is the logarithmic integral and pi(x) is the number of primes <= x.
12
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
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
KEYWORD
sign,look
STATUS
approved