A192596 Monotonic ordering of set S generated by these rules: if x and y are in S and 3x+4y is a prime, then 3x+4y is in S, and 1 is in S.

1, 7, 31, 97, 127, 409, 601, 769, 1231, 1657, 1831, 2017, 2311, 3079, 3169, 3457, 3631, 3697, 3943, 4201, 4999, 5479, 5521, 5881, 6079, 6151, 6607, 6961, 7057, 7129, 7321, 7417, 7687, 8089, 8161, 8431, 9127, 9241, 9337, 9511, 9631, 9871, 10009

Offset

1,2

Comments

See the discussions at A192476 and A192580.

Links

Table of n, a(n) for n=1..43.

Mathematica

start = {1}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, 3 x + 4 y], 3 x + 4 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]}]]]], # < 20000 &]];
t = FixedPoint[b, start]    (* A192596 *)
PrimePi[t]   (* A192597 *)

Crossrefs

Cf. A192574, A192580, A192597.

Sequence in context: A205801 A193437 A199921 * A055899 A218956 A139876

Adjacent sequences: A192593 A192594 A192595 * A192597 A192598 A192599

Keyword

nonn

Author

Clark Kimberling, Jul 05 2011

Status

approved