A192583 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, 6, and 8 are in S.

2, 4, 5, 6, 8, 11, 13, 17, 23, 31, 37, 41, 47, 53, 67, 79, 83, 89, 103, 107, 137, 139, 149, 167, 179, 223, 269, 283, 317, 359, 499, 557, 619, 643, 719, 823, 857, 1097, 1193, 1433, 1439, 1699, 1997, 2153, 2477, 2879, 3343, 4457, 6857, 7159, 8599, 12919, 41143

Offset

1,1

Comments

See the discussion at A192580.

Links

Table of n, a(n) for n=1..53.

Mathematica

start = {2, 4, 6, 8}; 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]  (* A192583 *)
PrimePi[t] (* A192530 Nonprimes 4, 6, 8 are represented by "next prime down". *)

Crossrefs

Cf. A192476.

Sequence in context: A284525 A353187 A099247 * A240064 A007192 A081354

Adjacent sequences: A192580 A192581 A192582 * A192584 A192585 A192586

Keyword

nonn,fini,full

Author

Clark Kimberling, Jul 04 2011

Status

approved