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

%I #4 Mar 30 2012 18:57:36

%S 1,3,7,11,23,31,47,71,103,127,151,167,191,263,311,383,431,503,631,647,

%T 743,863,887,911,967,983,1103,1151,1303,1487,1583,1607,1783,1823,1831,

%U 1847,1871,2087,2207,2311,2351,2423,2447,2543,2591,2687,2927,3023

%N Monotonic ordering of set S generated by these rules: if x and y are in S and 2x+y^2 is a prime, then 2x+y^2 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, 1000}];

%t f[x_, y_] := If[MemberQ[primes, 2 x + y^2], 2 x + 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]}]]]], # < 4000 &]];

%t t = FixedPoint[b, start] (* A192614 *)

%t PrimePi[t] (* A192615 *)

%Y Cf. A192476, A192580, A192615.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jul 05 2011