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 A237975 #7 Apr 06 2014 22:24:12
%S A237975 0,0,0,0,1,1,2,2,2,2,2,2,2,2,2,4,4,3,2,2,2,2,2,2,2,2,2,2,2,2,5,5,4,4,
%T A237975 3,3,5,5,4,4,5,5,5,5,5,4,4,4,5,5,5,3,3,3,5,5,5,4,4,4,5,5,5,6,9,5,5,5,
%U A237975 5,5,5,11,6,10,5,5,4,4,4,4,5,11,9,8,9,6,10,5,5,5,5,5,5,5,5,8,11,11,7,8
%N A237975 Least nonnegative integer m such that for some k = 1, ..., n there are exactly m^2 twin prime pairs not exceeding k*n.
%C A237975 The conjecture in A237840 implies that a(n) exists for any n > 0.
%H A237975 Zhi-Wei Sun, <a href="/A237975/b237975.txt">Table of n, a(n) for n = 1..10000</a>
%H A237975 Z.-W. Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641, 2014
%e A237975 a(7) = 2 since there are exactly 2^2 twin prime pairs not exceeding 3*7 = 21 (namely, {3, 5}, {5, 7}, {11, 13} and{17,19}), and the number of twin prime pairs not exceeding 1*7 or 2*7 is not a square.
%e A237975 a(18055) = 675 since there are exactly 675^2 = 455625 twin prime pairs not exceeding 5758*18055.
%t A237975 tw[0]:=0
%t A237975 tw[n_]:=tw[n-1]+If[PrimeQ[Prime[n]+2],1,0]
%t A237975 SQ[n_]:=IntegerQ[Sqrt[tw[PrimePi[n]]]]
%t A237975 Do[Do[If[SQ[k*n-2],Print[n," ",Sqrt[tw[PrimePi[k*n-2]]]];Goto[aa]],{k,1,n}];Print[n," ",0];Label[aa];Continue,{n,1,100}]
%Y A237975 Cf. A000290, A001359, A006512, A237840, A237879.
%K A237975 nonn
%O A237975 1,7
%A A237975 _Zhi-Wei Sun_, Feb 16 2014