A192580 -id:A192580 - cp's OEIS frontend

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

Clark Kimberling, Jul 05 2011

See the discussions at A192476 and A192580.

Cf. A192476, A192580.

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 *)

A192595 Index-list of the primes generated at A192594.

Original entry on oeis.org

0, 4, 8, 12, 14, 21, 22, 25, 29, 36, 38, 42, 44, 46, 48, 50, 53, 58, 63, 65, 67, 68, 73, 74, 75, 78, 80, 82, 84, 85, 88, 90, 93, 95, 99, 100, 101, 105, 106, 110, 112, 114, 115, 117, 121, 122, 125, 127, 129, 131, 133, 134, 136, 138, 141, 143, 145, 147, 149, 151

Offset: 1

Clark Kimberling, Jul 05 2011

nonn

The initial 1 is given an index of 0. All other terms of A192594 are primes: 7=p(4), 19=p(8), etc.

Cf. A192476, A192580, A192594.

Mathematica
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(See A192594.)
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cp's OEIS Frontend

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.

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