A192613 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2+2y^2 is a prime, then x^2+2y^2 is in S, and 1, 2, and 4 are in S.

1, 2, 3, 4, 11, 17, 19, 41, 139, 251, 307, 379, 587, 1699, 3371

Offset: 1

Author

Clark Kimberling, Jul 05 2011

Keywords

• nonn
• fini
• full

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192612, A192476, A192580.

Programs

Mathematica

start = {1, 2, 4}; primes = Table[Prime[n], {n, 1, 20000}];
f[x_, y_] := If[MemberQ[primes, x^2 + 2 y^2], x^2 + 2 y^2]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,
         Length[w]}]]]], # < 30000 &]];
t = FixedPoint[b, start] (* A192613 *)