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A053621 Nearest integer to n/(log(n)-1). 1

%I

%S -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,

%T 12,12,12,13,13,13,13,14,14,14,14,15,15,15,15,16,16,16,16,16,17,17,17,

%U 17,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,22,22,22

%N Nearest integer to n/(log(n)-1).

%C 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

%H Reinhard Zumkeller, <a href="/A053621/b053621.txt">Table of n, a(n) for n = 1..10000</a>

%H C. K. Caldwell, <a href="http://www.utm.edu/research/primes/howmany.shtml">How Many Primes Are There?</a>

%t Table[Round[n/(Log[n]-1)], {n,1,80}] (* _G. C. Greubel_, May 17 2019 *)

%o (Haskell)

%o a053621 = round . (\x -> x / (log x - 1)) . fromIntegral

%o -- _Reinhard Zumkeller_, Apr 30 2014

%o (PARI) vector(80, n, round(n/(log(n)-1))) \\ _G. C. Greubel_, May 17 2019

%o (MAGMA) [Round(n/(Log(n)-1)): n in [1..80]]; // _G. C. Greubel_, May 17 2019

%o (Sage) [round(n/(log(n)-1)) for n in (1..80)] # _G. C. Greubel_, May 17 2019

%Y Cf. A000720, A047784, A050499.

%K sign,changed

%O 1,2

%A _Henry Bottomley_, Mar 21 2000

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Last modified May 21 02:48 EDT 2019. Contains 323434 sequences. (Running on oeis4.)