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A190802
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Gauss' approximation for the number of primes below 10^n.
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10
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5, 29, 177, 1245, 9629, 78627, 664917, 5762208, 50849234, 455055614, 4118066400, 37607950280, 346065645809, 3204942065691, 29844571475287, 279238344248556, 2623557165610821, 24739954309690414, 234057667376222381, 2220819602783663483
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OFFSET
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1,1
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COMMENTS
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The offset logarithmic integral or Eulerian logarithmic integral Li(10^n)-Li(2), i.e., integral(2..x, dt/log(t)), appears in Gauss’s formula for counting prime numbers < 10^n and is sometimes referred to as the "European" definition. - Vladimir Pletser, Mar 17 2013
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REFERENCES
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Jonathan Borwein, David H. Bailey, "Mathematics by Experiment", A. K. Peters, 2004, p. 65 (Table 2.2).
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LINKS
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FORMULA
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a(n) = round(integral(dt/log(t),t=2..10^n)).
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MAPLE
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seq(round(evalf(integrate(1/log(t), t=2..10^n))), n=1..21);
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MATHEMATICA
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Table[Round[Integrate[1/Log[t], {t, 2, 10^n}]], {n, 20}] (* James C. McMahon, Feb 06 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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