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 A230217 #12 Sep 01 2023 11:06:10
%S A230217 5,7,11,13,17,31,41,47,53,61,73,83,101,103,131,151,157,167,193,223,
%T A230217 251,263,271,277,307,311,347,367,433,563,571,593,601,613,641,647,677,
%U A230217 733,823,857,977,1097,1117,1217,1223,1231,1291,1301,1361,1427
%N A230217 List of those primes p with p + 6 and 3*p + 8 also prime.
%C A230217 Clearly, no term is congruent to 4 modulo 5.
%C A230217 This sequence is interesting because of the conjecture in the comments in A230219.
%H A230217 Zhi-Wei Sun, <a href="/A230217/b230217.txt">Table of n, a(n) for n = 1..10000</a>
%e A230217 a(1) = 5 since neither 2 + 6 nor 3 + 6 is prime, but 5 + 6 = 11 and 3*5 + 8 = 23 are both prime.
%t A230217 PQ[p_]:=PrimeQ[p+6]&&PrimeQ[3p+8]
%t A230217 m=0
%t A230217 Do[If[PQ[Prime[n]],m=m+1;Print[m," ",Prime[n]]],{n,1,225}]
%t A230217 Select[Prime[Range[300]],AllTrue[{#+6,3#+8},PrimeQ]&] (* _Harvey P. Dale_, Sep 01 2023 *)
%Y A230217 Cf. A023201, A230219.
%K A230217 nonn
%O A230217 1,1
%A A230217 _Zhi-Wei Sun_, Oct 11 2013