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%I #4 Mar 30 2012 18:57:35
%S 2,4,5,6,8,11,13,17,23,31,37,41,47,53,67,79,83,89,103,107,137,139,149,
%T 167,179,223,269,283,317,359,499,557,619,643,719,823,857,1097,1193,
%U 1433,1439,1699,1997,2153,2477,2879,3343,4457,6857,7159,8599,12919,41143
%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 discussion at A192580.
%t start = {2, 4, 6, 8}; primes = Table[Prime[n], {n, 1, 10000}];
%t f[x_, y_] := If[MemberQ[primes, x*y + 1], x*y + 1]
%t b[x_] :=
%t Block[{w = x},
%t Select[Union[
%t Flatten[AppendTo[w,
%t Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
%t 10000000 &]];
%t t = FixedPoint[b, start] (* A192583 *)
%t PrimePi[t] (* A192530 Nonprimes 4,6,8 are represented by "next prime down". *)
%Y Cf. A192476.
%K nonn,fini,full
%O 1,1
%A _Clark Kimberling_, Jul 04 2011
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