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 A229989 #13 May 05 2019 03:24:40
%S A229989 0,2,2,3,4,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,7,7,7,6,7,7,7,7,8,8,8,9,9,9,
%T A229989 9,9,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,14,14,14,14,
%U A229989 14,14,14,14,13,14,14,14,15,16,16,16,17,18,18,18
%N A229989 Number of primes in the interval [floor(n/2), floor(3n/2)].
%C A229989 Conjectures:
%C A229989 (1) a(n+1) - a(n) = 1 for infinitely many n;
%C A229989 (2) a(n+1) - a(n) = -1 for infinitely many n;
%C A229989 (3) a(n+1) - a(n) = -1 if and only if n = 2*prime(m+1) - 1.
%H A229989 Nathaniel Johnston, <a href="/A229989/b229989.txt">Table of n, a(n) for n = 1..10000</a>
%e A229989 a(5) = 4 counts the primes in the interval [2,7].
%p A229989 with(numtheory): A229989 := proc(n) return pi(floor((3/2)*n))-pi(floor(n/2)-1): end proc: seq(A229989(n), n=1..75); # _Nathaniel Johnston_, Oct 11 2013
%t A229989 z = 1000; c[n_] := PrimePi[Floor[3 n/2]] - PrimePi[Floor[n/2]-1];
%t A229989 t = Table[c[n], {n, 1, z}]; (* A229989 *)
%t A229989 Flatten[Position[Differences[t], -1]] (* A076274? *)
%t A229989 Flatten[Position[Differences[t], 1]] (* A229990 *)
%Y A229989 Cf. A076274, A229990, A056172.
%K A229989 nonn,easy
%O A229989 1,2
%A A229989 _Clark Kimberling_, Oct 09 2013