A192612 - OEIS

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.

%I #5 Mar 30 2012 18:57:36

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

%N 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.

%C 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.

%t start = {1, 2}; primes = Table[Prime[n], {n, 1, 20000}];

%t f[x_, y_] := If[MemberQ[primes, x^2 + 2 y^2], x^2 + 2 y^2]

%t b[x_] :=

%t Block[{w = x},

%t Select[Union[

%t Flatten[AppendTo[w,

%t Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1,

%t Length[w]}]]]], # < 30000 &]];

%t t = FixedPoint[b, start] (* A192612 *)

%Y Cf. A192476, A192580, A192613.

%K nonn,full,fini

%O 1,2

%A _Clark Kimberling_, Jul 05 2011