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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 and 4 are in S.
2

%I #4 Mar 30 2012 18:57:35

%S 2,4,5,11,17,23,47

%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 and 4 are in S.

%C See the discussion at A192580. As sets, A192580 lies in A192581, which lies in A192582.

%t start = {2, 4}; 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 50000 &]];

%t t = FixedPoint[b, start] (* A192581 *)

%Y Cf. A192476, A192580.

%K nonn,fini,full

%O 1,1

%A _Clark Kimberling_, Jul 04 2011