A192530 -id:A192530 - cp's OEIS frontend

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

Clark Kimberling, Jul 04 2011

See the discussion at A192580.

Cf. A192476.

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". *)

A192529 Monotonic ordering of set S generated by these rules: if x and y are in S then 3xy-x-y is in S, and 2 is in S.

Original entry on oeis.org

2, 8, 38, 176, 188, 866, 878, 938, 4040, 4256, 4316, 4328, 4388, 4688, 19850, 19910, 20186, 20198, 21206, 21278, 21566, 21578, 21638, 21938, 23438, 92576, 92912, 97820, 97880, 98900, 99176, 99248, 99260, 99536, 99548, 100916, 100928, 100988

Offset: 1

Clark Kimberling, Jul 03 2011

nonn

Cf. A192472.

start = {2}; f[x_, y_] := 3 x*y - x - y
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      1000000 &]];
t = NestList[b, start, 12][[-1]] (* A192529 *)
t/2 (* A192530 *)
Table[t[[i]] - t[[i - 1]], {i, 2, Length[t]}] (* differences *)

cp's OEIS Frontend

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.

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