This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053621 #20 Feb 26 2024 03:53:22
%S A053621 -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 A053621 12,12,12,13,13,13,13,14,14,14,14,15,15,15,15,16,16,16,16,16,17,17,17,
%U A053621 17,18,18,18,18,19,19,19,19,19,20,20,20,20,20,21,21,21,21,22,22,22
%N A053621 Nearest integer to n/(log(n)-1).
%C A053621 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 A053621 Reinhard Zumkeller, <a href="/A053621/b053621.txt">Table of n, a(n) for n = 1..10000</a>
%H A053621 C. K. Caldwell, <a href="http://www.utm.edu/research/primes/howmany.shtml">How Many Primes Are There?</a>
%H A053621 Pierre Dusart, <a href="https://arxiv.org/abs/1002.0442">Estimates of Some Functions Over Primes without R.H.</a>, arXiv:1002.0442 [math.NT], 2010.
%t A053621 Table[Round[n/(Log[n]-1)], {n,1,80}] (* _G. C. Greubel_, May 17 2019 *)
%o A053621 (Haskell)
%o A053621 a053621 = round . (\x -> x / (log x - 1)) . fromIntegral
%o A053621 -- _Reinhard Zumkeller_, Apr 30 2014
%o A053621 (PARI) vector(80, n, round(n/(log(n)-1))) \\ _G. C. Greubel_, May 17 2019
%o A053621 (Magma) [Round(n/(Log(n)-1)): n in [1..80]]; // _G. C. Greubel_, May 17 2019
%o A053621 (Sage) [round(n/(log(n)-1)) for n in (1..80)] # _G. C. Greubel_, May 17 2019
%Y A053621 Cf. A000720, A047784, A050499, A053620.
%K A053621 sign
%O A053621 1,2
%A A053621 _Henry Bottomley_, Mar 21 2000