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 A189024 #12 Mar 26 2023 16:44:57
%S A189024 0,1,2,1,2,1,2,1,1,1,1,1,2,2,1,1,2,1,2,2,2,1,2,1,1,1,1,1,1,1,2,2,2,2,
%T A189024 1,1,2,1,1,1,2,2,3,2,2,2,3,2,2,2,1,1,2,2,1,1,1,1,2,2,2,2,2,2,2,2,3,2,
%U A189024 2,1,2,2,3,3,3,2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,2,2,1,1,2,2,3,3,3,3,4,3,4,4,4,3,4,3,3,3,3,2,2,1,1,1,1,1,0,0,1
%N A189024 Number of primes in the range (n - sqrt(n), n].
%C A189024 Note that the lower bound, n-sqrt(n), is excluded from the count and the upper range, n, is included. The last zero term appears to be a(126). See A189026 for special primes associated with this sequence. This sequence is related to Oppermann's conjecture that for any k > 1 there is a prime between k^2 - k and k^2.
%H A189024 T. D. Noe, <a href="/A189024/b189024.txt">Table of n, a(n) for n = 1..10000</a>
%H A189024 Wikipedia, <a href="http://en.wikipedia.org/wiki/Oppermann's_conjecture">Oppermann's conjecture</a>
%t A189024 cnt = 0; lastLower = 0; Table[lower = Floor[n - Sqrt[n]]; If[lastLower < lower && PrimeQ[lower], cnt--]; lastLower = lower; If[PrimeQ[n], cnt++]; cnt, {n, 100}]
%t A189024 Table[PrimePi[n]-PrimePi[n-Sqrt[n]],{n,130}] (* _Harvey P. Dale_, Mar 26 2023 *)
%Y A189024 Cf. A188817, A189025, A189027.
%K A189024 nonn
%O A189024 1,3
%A A189024 _T. D. Noe_, Apr 15 2011