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A191136 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x+1 and 4x+1 are in a.

%I A191136 #8 Jul 13 2013 12:04:10
%S A191136 1,4,5,13,16,17,21,40,49,52,53,64,65,69,85,121,148,157,160,161,193,
%T A191136 196,197,208,209,213,256,257,261,277,341,364,445,472,481,484,485,580,
%U A191136 589,592,593,625,628,629,640,641,645,769,772,773,784,785,789,832,833,837,853,1024,1025,1029,1045,1093,1109,1336,1365,1417,1444
%N A191136 Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 3x+1 and 4x+1 are in a.
%C A191136 See A191113.
%H A191136 Reinhard Zumkeller, <a href="/A191136/b191136.txt">Table of n, a(n) for n = 1..10000</a>
%t A191136 h = 3; i = 1; j = 4; k = 1; f = 1; g = 9;
%t A191136 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]   (* A191136 *)
%t A191136 b = (a - 1)/3; c = (a - 1)/4; r = Range[1, 1500];
%t A191136 d = Intersection[b, r] (* A191196 *)
%t A191136 e = Intersection[c, r] (* A191197 *)
%o A191136 (Haskell)
%o A191136 import Data.Set (singleton, deleteFindMin, insert)
%o A191136 a191136 n = a191136_list !! (n-1)
%o A191136 a191136_list = f $ singleton 1
%o A191136    where f s = m : (f $ insert (3*m+1) $ insert (4*m+1) s')
%o A191136              where (m, s') = deleteFindMin s
%o A191136 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A191136 Cf. A191113.
%K A191136 nonn
%O A191136 1,2
%A A191136 _Clark Kimberling_, May 28 2011