A192612 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 and 2 are in S.

1, 2, 3, 11, 17, 19, 139, 251, 307, 379, 587

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..11.

Mathematica

start = {1, 2}; 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]  (* A192612 *)

Crossrefs

Cf. A192476, A192580, A192613.

Sequence in context: A051098 A215811 A051076 * A014092 A100962 A045337

Adjacent sequences: A192609 A192610 A192611 * A192613 A192614 A192615

Keyword

nonn,full,fini

Author

Clark Kimberling, Jul 05 2011

Status

approved