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A052435
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a(n) = round(li(n) - pi(n)), where li is the logarithmic integral and pi(x) is the number of primes <= x.
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12
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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
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2,8
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COMMENTS
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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
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LINKS
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MATHEMATICA
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Table[Round[LogIntegral[x]-PrimePi[x]], {x, 2, 100}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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