A192594 Monotonic ordering of set S generated by these rules: if x and y are in S and 5x+2y is a prime, then 5x+2y is in S, and 1 is in S.

1, 7, 19, 37, 43, 73, 79, 97, 109, 151, 163, 181, 193, 199, 223, 229, 241, 271, 307, 313, 331, 337, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 613, 619, 631, 643, 661, 673, 691, 709, 727, 739, 751, 757, 769

Offset: 1

Author

Clark Kimberling, Jul 05 2011

Keywords

• nonn

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192595, A192476, A192580.

Programs

Mathematica

start = {1}; primes = Table[Prime[n], {n, 1, 1000}];
f[x_, y_] := If[MemberQ[primes, 5 x + 2 y], 5 x + 2 y]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
         Length[w]}]]]], # < 2000 &]];
t = FixedPoint[b, start]    (* A192594 *)
PrimePi[t]    (* A192595 *)