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 A215684 #14 Apr 06 2019 10:32:28
%S A215684 3,5,7,17,67,107,277,353,487,557,787,797,853,983,1033,1163,1597,1637,
%T A215684 1657,1697,1867,1913,2347,2543,2833,2897,2953,2957,3343,3413,3607,
%U A215684 3623,3643,3863,3907,4013,4447,4583,4987,5087,5113,5507,6277,6653,7027,7433,7603
%N A215684 Let p=prime=a(n); then a(n+1) = smallest prime q>p such that 2p+q and 2q+p are both primes.
%H A215684 Zak Seidov, <a href="/A215684/b215684.txt">Table of n, a(n) for n = 1..1000</a>
%e A215684 2*3+5=11 and 2*5+3=13 are both prime, so a(2) = 5.
%e A215684 2*7+17=31 and 2*17+7=41 are both prime, so a(4) = 17.
%t A215684 a=3;s={a};m=100;Do[n1=PrimePi[a]+1;Do[b=Prime[n];If[PrimeQ[2*a+b]&&PrimeQ[2*b+a],AppendTo[s,b];a=b;Break[]],{n,n1,n1+100000}],{m-1}];s
%t A215684 spq[n_]:=Module[{p=NextPrime[n]},While[!PrimeQ[2n+p]||!PrimeQ[2p+n],p=NextPrime[p]];p]; NestList[spq,3,50] (* _Harvey P. Dale_, Apr 06 2019 *)
%Y A215684 Cf. A181848.
%K A215684 nonn
%O A215684 1,1
%A A215684 _Zak Seidov_, Aug 20 2012