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 A230022 #17 Apr 04 2014 18:45:03
%S A230022 1,1,2,2,3,3,3,4,3,4,5,5,4,5,4,5,5,6,7,6,5,6,6,6,5,5,7,6,6,7,7,6,6,7,
%T A230022 7,8,9,8,9,9,8,8,8,9,8,9,9,8,10,10,9,10,9,10,10,10,10,11,10,10,9,10,9,
%U A230022 11,10,11,11,11,11,11,11,11,10,12,11,10,11,12,13,11
%N A230022 a(n) = |{the number of primes in the interval (k*n, (k+1)*n]: k = 0, 1, ..., n-1}|.
%C A230022 Conjecture: (i) a(n) is at least sqrt(n-1) for each n > 0, and equality holds only when n is 2 or 26.
%C A230022 (ii) The sequence contains all positive integers.
%C A230022 We have verified part (i) of the conjecture for n up to 10000.
%H A230022 Zhi-Wei Sun, <a href="/A230022/b230022.txt">Table of n, a(n) for n = 1..4000</a>
%H A230022 Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
%e A230022 a(1) = 1 since the interval (0,1*1] contains no prime, and the set {0} has cardinaly 1.
%e A230022 a(3) = 2 since the intervals (0, 1*3], (1*3, 2*3], (2*3, 3*3] contain exactly 2, 1, 1 primes respectively, and the set {2, 1, 1} has cardinality 2.
%t A230022 d[k_,n_]:=PrimePi[(k+1)*n]-PrimePi[k*n]
%t A230022 a[n_]:=Length[Union[Table[d[k,n],{k,0,n-1}]]]
%t A230022 Table[a[n],{n,1,80}]
%Y A230022 Cf. A000040, A000720, A238277, A238278, A238281.
%K A230022 nonn
%O A230022 1,3
%A A230022 _Zhi-Wei Sun_, Feb 23 2014