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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.
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%I #7 Mar 21 2013 13:13:38

%S 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 137,151,163,173,257,281,401,487,547,617,677,691,821,823,977,1093,

%U 1123,1303,1381,2467,2707,3701,3907,4933,4937,5413,5527,5861,6737,7817

%N 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 See the discussions at A192476 and A192580.

%C Last term is a(61) = 62533. - _Giovanni Resta_, Mar 21 2013

%H Giovanni Resta, <a href="/A192588/b192588.txt">Table of n, a(n) for n = 1..61</a> (full sequence)

%t 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 Cf. A192476, A192580, A192586, A192587.

%K nonn,fini,full

%O 1,1

%A _Clark Kimberling_, Jul 05 2011