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A053621
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Nearest integer to n/(log(n)-1).
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1
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-1, -7, 30, 10, 8, 8, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22
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OFFSET
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1,2
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COMMENTS
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n/(log(n)-1) is a better approximation than n/log(n) to pi(n) the number of primes <= n, though worse than the logarithmic integral or the Riemann prime number formula.
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LINKS
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MATHEMATICA
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Table[Round[n/(Log[n]-1)], {n, 1, 80}] (* G. C. Greubel, May 17 2019 *)
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PROG
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(Haskell)
a053621 = round . (\x -> x / (log x - 1)) . fromIntegral
(PARI) vector(80, n, round(n/(log(n)-1))) \\ G. C. Greubel, May 17 2019
(Magma) [Round(n/(Log(n)-1)): n in [1..80]]; // G. C. Greubel, May 17 2019
(Sage) [round(n/(log(n)-1)) for n in (1..80)] # G. C. Greubel, May 17 2019
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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