A192582 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, and 6 are in S.

2, 4, 5, 6, 11, 13, 17, 23, 31, 37, 47, 53, 67, 79, 103, 107, 139, 149, 223, 269, 283, 317, 557, 619, 643, 1699, 2477, 3343

Offset: 1

Author

Clark Kimberling, Jul 04 2011

Keywords

• nonn
• fini
• full

Comments

See the discussion at A192580.

Crossrefs

Cf. A192476.

Programs

Mathematica

start = {2, 4, 6}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, x*y + 1], x*y + 1]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      10000000 &]];
t = FixedPoint[b, start]  (* A192582 *)