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 A063091 #20 Oct 16 2019 01:29:36
%S A063091 2,3,5,11,17,29,41,59,71,101,107,137,149,179,191,197,227,239,269,281,
%T A063091 283,311,317,337,347,419,431,461,521,547,569,577,599,617,641,659,773,
%U A063091 787,809,821,827,857,863,881,1019,1031,1049,1061,1091,1129,1151,1153
%N A063091 Prime(n) such that gcd(1+prime(n+1), 1+prime(n)) = gcd(-1+prime(n+1), -1+prime(n)).
%H A063091 Harry J. Smith, <a href="/A063091/b063091.txt">Table of n, a(n) for n = 1..1000</a>
%e A063091 p=101 is here because gcd(102,104) = 2 = gcd(100,102).
%t A063091 lst={};Do[p0=Prime[n];p1=Prime[n+1];If[GCD[p0-1,p1-1]==GCD[p0+1,p1+1],AppendTo[lst,p0]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 11 2010 *)
%t A063091 Transpose[Select[Partition[Prime[Range[200]],2,1],GCD[First[#]+1, Last[#]+1] == GCD[First[#]-1,Last[#]-1]&]][[1]] (* _Harvey P. Dale_, Jan 22 2012 *)
%o A063091 (PARI) { n=0; for (m=1, 10^9, if(gcd(prime(m+1) + 1, prime(m) + 1) == gcd(prime(m+1) - 1, prime(m) - 1), write("b063091.txt", n++, " ", prime(m)); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 17 2009
%Y A063091 Cf. A058263.
%K A063091 nonn
%O A063091 1,1
%A A063091 _Labos Elemer_, Aug 06 2001