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

1,2

Comments

See the discussions at A192476 and A192580.

Links

Table of n, a(n) for n=1..5.

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 *)

Crossrefs

Cf. A192476, A192580.

Sequence in context: A088733 A128996 A196174 * A075226 A192598 A028978

Adjacent sequences: A192588 A192589 A192590 * A192592 A192593 A192594

Keyword

nonn,fini,full

Author

Clark Kimberling, Jul 05 2011

Status

approved