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A192589 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. 1

%I

%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

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Last modified August 16 20:22 EDT 2022. Contains 356169 sequences. (Running on oeis4.)