A192530 Index-list (modified) of the primes generated at A192583.

1, 2, 3, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15, 16, 19, 22, 23, 24, 27, 28, 33, 34, 35, 39, 41, 48, 57, 61, 66, 72, 95, 102, 114, 117, 128, 143, 148, 184, 196, 227, 228, 266, 302, 325, 367, 417, 471, 606, 882, 916, 1071, 1539, 4305

Offset: 1

Author

Clark Kimberling, Jul 04 2011

Keywords

• nonn
• fini
• full

Comments

Besides the generated primes 2,5,11,13,17,..., the initial numbers 4,6,8 in A192583 are represented here by index of nearest lower prime.

Examples

			A192583=(2,4,5,6,8,11,13,17,23,...).  a(1)=1 because the index of 2 is 1; a(2)=2 because, for term #2 of A192530, which is 4, the nearest prime <4 is 3, which has index 2; a(3)=3 because the index of 5 is 3.  ("Nearest prime down" for nonprimes is given by PrimePi in the Mathematica program.)
		

Crossrefs

Cf. A192583.

Programs

Mathematica

start = {2, 4, 6, 8}; primes = Table[Prime[n], {n, 1, 10000}];
f[x_, y_] := If[MemberQ[primes, x*y + 1], x*y + 1]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      10000000 &]];
t = FixedPoint[b, start]  (* A192583 *)
PrimePi[t] (* A192530 Nonprimes 4,6,8 are represented by "next prime down". *)