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 A192588 #7 Mar 21 2013 13:13:38
%S A192588 2,3,4,5,6,7,8,11,13,17,19,23,29,31,37,41,43,47,61,67,73,101,103,113,
%T A192588 137,151,163,173,257,281,401,487,547,617,677,691,821,823,977,1093,
%U A192588 1123,1303,1381,2467,2707,3701,3907,4933,4937,5413,5527,5861,6737,7817
%N A192588 Monotonic ordering of set S generated by these rules: if x and y are in S and xy-1 is a prime, then xy-1 is in S, and 2, 4, 6, and 8 are in S.
%C A192588 See the discussions at A192476 and A192580.
%C A192588 Last term is a(61) = 62533. - _Giovanni Resta_, Mar 21 2013
%H A192588 Giovanni Resta, <a href="/A192588/b192588.txt">Table of n, a(n) for n = 1..61</a> (full sequence)
%t A192588 start = {2, 4, 6, 8}; seq = {}; new = start; While[new != {}, seq = Union[seq, new]; fresh = new; new = {}; Do[If[PrimeQ[u = x*y - 1], If[! MemberQ[seq, u], AppendTo[new, u]]], {x, seq}, {y, fresh}]]; seq (* _Giovanni Resta_, Mar 21 2013 *)
%Y A192588 Cf. A192476, A192580, A192586, A192587.
%K A192588 nonn,fini,full
%O A192588 1,1
%A A192588 _Clark Kimberling_, Jul 05 2011