A192598 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 is in S.

1, 3, 11, 19, 139, 251, 379

Offset

1,2

Comments

See the discussions at A192476 and A192580. The start-set for A192598 is {1}. For results using start-sets {1,2}, and {1,2,4}, see A192612 and A192613.

Links

Table of n, a(n) for n=1..7.

Mathematica

start = {1}; 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]  (* A192598 *)

Crossrefs

Cf. A192476, A192580, A192612, A192613.

Sequence in context: A196174 A192591 A075226 * A028978 A082628 A279257

Adjacent sequences: A192595 A192596 A192597 * A192599 A192600 A192601

Keyword

nonn,fini,full

Author

Clark Kimberling, Jul 05 2011

Status

approved