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A191143 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x+2 and 4x+1 are in a.

%I A191143 #11 Jul 13 2013 12:04:11
%S A191143 1,5,17,21,53,65,69,85,161,197,209,213,257,261,277,341,485,593,629,
%T A191143 641,645,773,785,789,833,837,853,1025,1029,1045,1109,1365,1457,1781,
%U A191143 1889,1925,1937,1941,2321,2357,2369,2373,2501,2513,2517,2561,2565,2581,3077,3089,3093,3137,3141,3157,3329,3333,3349,3413,4097,4101
%N A191143 Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 3x+2 and 4x+1 are in a.
%C A191143 See A191113.
%H A191143 Reinhard Zumkeller, <a href="/A191143/b191143.txt">Table of n, a(n) for n = 1..10000</a>
%t A191143 h = 3; i = 2; j = 4; k = 1; f = 1; g = 9;
%t A191143 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191143 *)
%t A191143 b = (a - 2)/3; c = (a - 1)/4; r = Range[1, 1500];
%t A191143 d = Intersection[b, r] (* A191210 *)
%t A191143 e = Intersection[c, r] (* A191136 *)
%t A191143 m = (a + 1)/2 (* divisibility property *)
%t A191143 p = (a + 3)/4 (* divisibility property *)
%o A191143 (Haskell)
%o A191143 import Data.Set (singleton, deleteFindMin, insert)
%o A191143 a191143 n = a191143_list !! (n-1)
%o A191143 a191143_list = f $ singleton 1
%o A191143    where f s = m : (f $ insert (3*m+2) $ insert (4*m+1) s')
%o A191143              where (m, s') = deleteFindMin s
%o A191143 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A191143 Cf. A191113.
%K A191143 nonn
%O A191143 1,2
%A A191143 _Clark Kimberling_, May 28 2011