A192614 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.

1, 3, 7, 11, 23, 31, 47, 71, 103, 127, 151, 167, 191, 263, 311, 383, 431, 503, 631, 647, 743, 863, 887, 911, 967, 983, 1103, 1151, 1303, 1487, 1583, 1607, 1783, 1823, 1831, 1847, 1871, 2087, 2207, 2311, 2351, 2423, 2447, 2543, 2591, 2687, 2927, 3023

Offset: 1

Author

Clark Kimberling, Jul 05 2011

Keywords

• nonn

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192476, A192580, A192615.

Programs

Mathematica

start = {1}; primes = Table[Prime[n], {n, 1, 1000}];
f[x_, y_] := If[MemberQ[primes, 2 x + y^2], 2 x + 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]}]]]], # < 4000 &]];
t = FixedPoint[b, start]  (* A192614 *)
PrimePi[t]   (* A192615 *)