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A192583 Monotonic ordering of set S generated by these rules:  if x and y are in S and xy+1 is a prime, then xy+1 is in S, and 2, 4, 6, and 8 are in S. 4

%I

%S 2,4,5,6,8,11,13,17,23,31,37,41,47,53,67,79,83,89,103,107,137,139,149,

%T 167,179,223,269,283,317,359,499,557,619,643,719,823,857,1097,1193,

%U 1433,1439,1699,1997,2153,2477,2879,3343,4457,6857,7159,8599,12919,41143

%N Monotonic ordering of set S generated by these rules: if x and y are in S and xy+1 is a prime, then xy+1 is in S, and 2, 4, 6, and 8 are in S.

%C See the discussion at A192580.

%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. A192476.

%K nonn,fini,full

%O 1,1

%A _Clark Kimberling_, Jul 04 2011

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Last modified August 9 17:13 EDT 2022. Contains 356026 sequences. (Running on oeis4.)