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 A260882 #11 Aug 02 2015 22:26:10
%S A260882 3,47,3,13,797,89,2269,733,7877,53,14683,16267,17167,59951,10067,761,
%T A260882 94463,12437,124561,71881,52009,6791,10061,47287,10789,19009,4813,
%U A260882 23173,27427,18701,23011,44917,17,70937,883,727,99079,10531,18749,126541,18121,34807,29873,159473,853,165317,80627,159721,8263,411707
%N A260882 Least prime p such that 2*prime(p*n)+1 = prime(q*n) for some prime q.
%C A260882 Conjecture: a(n) exists for any n > 0. In general, if a > 1 and b are integers with a+b odd and gcd(a,b)=1, then for any positive integer n there are primes p and q such that a*prime(p*n)+b = prime(q*n).
%C A260882 This is a supplement to the conjecture in A260120. It implies that there are infinitely many Sophie Germain primes.
%H A260882 Zhi-Wei Sun, <a href="/A260882/b260882.txt">Table of n, a(n) for n = 1..200</a>
%H A260882 Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, arXiv:1211.1588 [math.NT], 2012-2015.
%e A260882 a(2) = 47 since 2*prime(47*2)+1 = 2*491+1 = 983 = prime(83*2) with 47 and 83 both prime.
%e A260882 a(199) = 2784167 since 2*prime(2784167*199)+1 = 2*12290086499+1 = 24580172999 = prime(5399231*199) with 2784167 and 5399231 both prime.
%t A260882 f[n_]:=Prime[n]
%t A260882 PQ[p_,n_]:=PrimeQ[p]&&PrimeQ[PrimePi[p]/n]
%t A260882 Do[k=0;Label[bb];k=k+1;If[PQ[2*f[n*f[k]]+1,n],Goto[aa],Goto[bb]];Label[aa];Print[n," ", f[k]];Continue,{n,1,50}]
%Y A260882 Cf. A000040, A005384, A260120, A260252.
%K A260882 nonn
%O A260882 1,1
%A A260882 _Zhi-Wei Sun_, Aug 02 2015