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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A091207 A284525 A099247 * A240064 A007192 A081354

Adjacent sequences:  A192580 A192581 A192582 * A192584 A192585 A192586

KEYWORD

nonn,fini,full

AUTHOR

Clark Kimberling, Jul 04 2011

STATUS

approved

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Last modified February 26 08:33 EST 2020. Contains 332277 sequences. (Running on oeis4.)