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 A079010 #12 Feb 11 2021 23:01:00
%S A079010 6,14,14,8,8,14,18,14,18,8,24,8,8,8,18,44,24,38,18,30,14,14,8,14,18,8,
%T A079010 8,8,30,8,38,18,14,14,66,36,26,30,30,8,18,14,8,50,18,18,14,8,66,26,14,
%U A079010 44,38,54,18,18,38,30,8,30,14,24,26,8,26,14,8,8,60,26
%N A079010 a(n) = nextprime(16 + A022008(n)) - (16 + A022008(n)).
%C A079010 a(n) is the prime difference d >= 6, following [42424] difference pattern defining A022008.
%e A079010 n=2: A022008(2)=97, corresponding sextuplet is {97, 101, 103, 107, 109, 113=97+16}, nextprime(113) - 113 = 127 - 113 = 14, so a(2)=14. Constraints for present terms: (a) are incongruent to 4 modulo 6; (b) Mod(a(n), 30) = {0, 6, 8, 14, 18, 20, 24, 26}; 6 occurs only once; (c) further prohibited values like e.g. 20 etc.
%t A079010 d[x_] := Prime[x+1]-Prime[x]; Do[If[Equal[d[n], 4]&&Equal[d[n+1], 2]&& Equal[d[n+2], 4]&&Equal[d[n+3], 2]&& Equal[d[n+4], 4], Print[d[n+5]]], {n, 1, 100000}]
%Y A079010 Cf. A022008.
%K A079010 nonn
%O A079010 1,1
%A A079010 _Labos Elemer_, Jan 21 2003