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 A209617 #19 Apr 30 2016 17:52:16
%S A209617 23,37,47,53,67,79,83,89,97,113,127,131,157,163,167,173,211,223,233,
%T A209617 257,263,277,307,317,331,353,359,367,373,379,383,389,397,401,439,443,
%U A209617 449,457,467,479,487,491,499,503,509,541,563,593,607,613,647,653,673,677
%N A209617 Primes separated from their adjacent primes on both sides by a prime number of successive composites.
%C A209617 Intersection of A209623 and A209624.
%H A209617 Charles R Greathouse IV, <a href="/A209617/b209617.txt">Table of n, a(n) for n = 1..10000</a>
%e A209617 a(1)=23 is the first prime separated both from its previous prime neighbor (19) and next prime neighbor (29) by a prime number (respectively 3 and 5) of composites: [19], 20, 21, 22, [23], 24, 25, 26, 27, 28, [29].
%t A209617 d = Differences[Prime[Range[200]]] - 1; t = {}; Do[If[PrimeQ[d[[i - 1]]] && PrimeQ[d[[i]]], AppendTo[t, Prime[i]]], {i, 2, Length[d]}]; t (* _T. D. Noe_, Mar 18 2012 *)
%o A209617 (PARI) list(lim)=my(v=List(),p=2,q=3); forprime(r=5,nextprime(lim\1+1), if(isprime(q-p-1) && isprime(r-q-1), listput(v,q)); p=q; q=r); Vec(v) \\ _Charles R Greathouse IV_, Apr 30 2016
%Y A209617 Cf. A209623, A209624.
%K A209617 nonn
%O A209617 1,1
%A A209617 _Lekraj Beedassy_, Mar 12 2012