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 A260219 #13 Jul 20 2015 01:48:14
%S A260219 3,47,229,379,11,2687,1181,24547,5,509,5,16619,877,22543,3,9067,60337,
%T A260219 10667,997,24061,18329,56099,1787,58757,108883,416881,157141,11003,
%U A260219 14939,113167,101957,77969,613,27947,52153,158551,6197,36607,25237,27179,330689,203617,77419,708269,87649,340381,267601,67153,123377,21617
%N A260219 Least prime p such that pi(p*n)^2 + 1 = prime(q*n) for some prime q.
%C A260219 Conjecture: a(n) exists for any n > 0. In general, if a,b,c are integers with a > 0 and gcd(a,b,c) = 1, and a+b or c is odd, and b^2 - 4*a*c is not a square, then there are primes p and q such that a*pi(p*n)^2 + b*pi(p*n) + c = prime(q*n).
%D A260219 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 A260219 Zhi-Wei Sun, <a href="/A260219/b260219.txt">Table of n, a(n) for n = 1..72</a>
%H A260219 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 A260219 a(1) = 3 since pi(3*1)^2 + 1 = 5 = prime(3*1) with 3 prime.
%e A260219 a(8) = 24547 since pi(24547*8)^2 + 1 = 17686^2 + 1 = 312794597 = prime(2113417*8) with 24547 and 2113417 both prime.
%t A260219 PQ[n_, p_] := PrimeQ[p] && PrimeQ[PrimePi[p]/n]; Do[k = 0; Label[bb]; k = k + 1; If[PQ[n, PrimePi[Prime[k] * n]^2 + 1], Goto[aa], Goto[bb]]; Label[aa]; Print[n, " ", Prime[k]]; Continue,{n, 50}]
%o A260219 (PARI) first(m)={my(v=vector(m),p,q,n);for(n=1,m,p=0;while(1,p++;q=1;while(primepi(prime(p)*n)^2 +1 >= prime(prime(q)*n), if(primepi(prime(p)*n)^2 +1 == prime(prime(q)*n),v[n]=prime(p);break(2),q++;))));v;} /* _Anders Hellström_, Jul 19 2015 */
%Y A260219 Cf. A000040, A000720, A002496, A259731, A260120, A260197.
%K A260219 nonn
%O A260219 1,1
%A A260219 _Zhi-Wei Sun_, Jul 19 2015