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.

2, 4, 7, 11, 17, 19, 31, 37, 41, 47, 71, 79, 97, 127, 151, 167, 191, 197, 257, 337, 397, 607, 677, 797, 1031, 1217, 1597, 2437, 2711, 3191, 4127, 4871, 4877, 10847, 43391

Offset: 1

Author

Clark Kimberling, Jul 05 2011

Keywords

• nonn
• fini
• full

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192476 and A192580.

Programs

Mathematica

start = {2, 4}; primes = Table[Prime[n], {n, 1, 40000}];
f[x_, y_] := If[MemberQ[primes, x*y + 3], x*y + 3]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      200000 &]];
t = FixedPoint[b, start]    (* A192589 *)