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 A260140 #16 Aug 02 2015 13:34:14
%S A260140 2,5,19,3187,11,2251,12149,19,239,23761,61,157,8419,10973,1117,9601,
%T A260140 58741,37,53359,14533,1063,934811,78487,27647,1249,720221,1616077,
%U A260140 30091,5501,131627,2003,67,677,1313843,45413,273943,127241,19661,188317,811,33863,17789,109073,602269,125201,6424897,441647,2512897,2909,836471
%N A260140 Least prime p such that pi(p*n) = pi(q*n)^2 for some prime q, where pi(x) denotes the number of primes not exceeding x.
%C A260140 Conjecture: a(n) exists for any n > 0. In general, for any integers a,b,c,n with a > 0 and n > 0, there are two elements x and y of the set {pi(p*n): p is prime} with a*x^2+b*x+c = y.
%C A260140 A supplement to the conjecture: For any integers b,c,n with b > 0 and n > 0, we have b*x+c = y for some elements x and y of the set {pi(p*n): p is prime}. - _Zhi-Wei Sun_, Aug 02 2015
%D A260140 Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.
%H A260140 Zhi-Wei Sun, <a href="/A260140/b260140.txt">Table of n, a(n) for n = 1..150</a>
%H A260140 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1402.6641">Problems on combinatorial properties of primes</a>, arXiv:1402.6641 [math.NT], 2014.
%e A260140 a(1) = 2 since pi(2*1) = 1^2 = pi(2*1)^2 with 2 prime.
%e A260140 a(4) = 3187 since pi(3187*4) = 1521 = 39^2 = pi(43*4)^2 with 43 and 3187 both prime.
%e A260140 a(72) = 25135867 since pi(25135867*72) = 89321401 = 9451^2 = pi(1367*72)^2 with 1367 and 25135867 both prime.
%e A260140 a(84) = 106788581 since pi(106788581*84) = 410224516 = 20254^2 = prime(2713*84)^2 with 2713 and 106788581 both prime.
%t A260140 SQ[n_]:=IntegerQ[Sqrt[n]]
%t A260140 f[n_]:=PrimePi[n]
%t A260140 Do[k=0;Label[bb];k=k+1;If[SQ[f[Prime[k]*n]]==False,Goto[bb]];Do[If[Sqrt[f[Prime[k]*n]]==f[Prime[j]*n],Goto[aa]];If[Sqrt[f[Prime[k]*n]]<f[Prime[j]*n],Goto[bb]];Continue,{j,1,k}];Goto[bb]; Label[aa];Print[n," ",Prime[k]];Continue,{n,1,50}]
%Y A260140 Cf. A000040, A000290, A000720, A257364, A257928, A260120.
%K A260140 nonn
%O A260140 1,1
%A A260140 _Zhi-Wei Sun_, Jul 17 2015