A192591 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, 3, 11, 19, 131

Offset: 1

Author

Clark Kimberling, Jul 05 2011

Keywords

• nonn
• fini
• full

Comments

See the discussions at A192476 and A192580.

Crossrefs

Cf. A192476, A192580.

Programs

Mathematica

start = {1}; primes = Table[Prime[n], {n, 1, 40000}];
f[x_, y_] := If[MemberQ[primes, x^2 + y^2 + 1], x^2 + y^2 + 1]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      200000 &]];
t = FixedPoint[b, start]    (* A192591 *)