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%I #6 Jul 16 2015 22:08:02
%S 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,
%T 57,61,66,72,95,102,114,117,128,143,148,184,196,227,228,266,302,325,
%U 367,417,471,606,882,916,1071,1539,4305
%N Index-list (modified) of the primes generated at A192583.
%C 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.
%e 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.)
%t start = {2, 4, 6, 8}; primes = Table[Prime[n], {n, 1, 10000}];
%t f[x_, y_] := If[MemberQ[primes, x*y + 1], x*y + 1]
%t b[x_] :=
%t Block[{w = x},
%t Select[Union[
%t Flatten[AppendTo[w,
%t Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
%t 10000000 &]];
%t t = FixedPoint[b, start] (* A192583 *)
%t PrimePi[t] (* A192530 Nonprimes 4,6,8 are represented by "next prime down". *)
%Y Cf. A192583.
%K nonn,fini,full
%O 1,2
%A _Clark Kimberling_, Jul 04 2011
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