A192592 Monotonic ordering of set S generated by these rules: if x and y are in S and 3x+2y is a prime, then 3x+2y is in S, and 1 is in S.

1, 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557, 569, 577, 593, 601, 613, 617

Offset: 1

Author

Clark Kimberling, Jul 05 2011

Keywords

• nonn

Comments

See the discussions at A192476 and A192580.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..609

Crossrefs

Cf. A192476, A192580, A192593.

Programs

Mathematica

start = {1}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, 2 x + 3 y], 2 x + 3 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]}]]]], # < 1000 &]];
t = FixedPoint[b, start]     (* A192592 *)
PrimePi[t]    (* A192593 *)