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

%I #4 Mar 30 2012 18:57:35

%S 1,3,11,19,131

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

%C See the discussions at A192476 and A192580.

%t start = {1}; primes = Table[Prime[n], {n, 1, 40000}];

%t f[x_, y_] := If[MemberQ[primes, x^2 + y^2 + 1], x^2 + y^2 + 1]

%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, i}]]]], # <

%t 200000 &]];

%t t = FixedPoint[b, start] (* A192591 *)

%Y Cf. A192476, A192580.

%K nonn,fini,full

%O 1,2

%A _Clark Kimberling_, Jul 05 2011