A192589 - OEIS

%I #6 Jan 03 2014 15:57:39

%S 2,4,7,11,17,19,31,37,41,47,71,79,97,127,151,167,191,197,257,337,397,

%T 607,677,797,1031,1217,1597,2437,2711,3191,4127,4871,4877,10847,43391

%N Monotonic ordering of set S generated by these rules:  if x and y are in S and xy+3 is a prime, then xy+3 is in S, and 2 and 4 are in S.

%C See the discussions at A192476 and A192580.

%t start = {2, 4}; primes = Table[Prime[n], {n, 1, 40000}];

%t f[x_, y_] := If[MemberQ[primes, x*y + 3], x*y + 3]

%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       200000 &]];

%t t = FixedPoint[b, start]    (* A192589 *)

%Y Cf. A192476 and A192580.

%K nonn,fini,full

%O 1,1

%A _Clark Kimberling_, Jul 05 2011