A192592 - OEIS

%I #8 May 08 2017 09:22:52

%S 1,5,13,17,29,37,41,53,61,73,89,97,109,113,137,149,157,173,181,193,

%T 197,229,233,241,257,269,277,281,293,313,317,337,349,353,373,389,397,

%U 401,409,421,433,449,457,461,509,521,541,557,569,577,593,601,613,617

%N Monotonic ordering of set S generated by these rules:  if x and y are in S and 3x+2y is a prime, then 3x+2y is in S, and 1 is in S.

%C See the discussions at A192476 and A192580.

%H Vincenzo Librandi, <a href="/A192592/b192592.txt">Table of n, a(n) for n = 1..609</a>

%t start = {1}; primes = Table[Prime[n], {n, 1, 10000}];

%t f[x_, y_] := If[MemberQ[primes, 2 x + 3 y], 2 x + 3 y]

%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,

%t          Length[w]}]]]], # < 1000 &]];

%t t = FixedPoint[b, start]     (* A192592 *)

%t PrimePi[t]    (* A192593 *)

%Y Cf. A192476, A192580, A192593.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jul 05 2011