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A191122 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-1 and 4x are in a.

%I A191122 #10 Jul 13 2013 12:04:10
%S A191122 1,2,4,5,8,11,14,16,20,23,32,41,44,47,56,59,64,68,80,92,95,122,128,
%T A191122 131,140,164,167,176,188,191,203,224,236,239,256,272,275,284,320,365,
%U A191122 368,380,383,392,419,488,491,500,512,524,527,560,563,572,608,656,668,671,704,707,716,752,764,767,812,815,824,851,896,944,956,959
%N A191122 Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 3x-1 and 4x are in a.
%C A191122 See A191113.
%H A191122 Reinhard Zumkeller, <a href="/A191122/b191122.txt">Table of n, a(n) for n = 1..10000</a>
%t A191122 h = 3; i = -1; j = 4; k = 0; f = 1; g = 9;
%t A191122 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191122 *)
%t A191122 b = (a + 1)/3; c = a/4; r = Range[1, 1500];
%t A191122 d = Intersection[b, r] (* A191168 *)
%t A191122 e = Intersection[c, r] (* A191169 *)
%o A191122 (Haskell)
%o A191122 import Data.Set (singleton, deleteFindMin, insert)
%o A191122 a191122 n = a191122_list !! (n-1)
%o A191122 a191122_list = f $ singleton 1
%o A191122    where f s = m : (f $ insert (3*m-1) $ insert (4*m) s')
%o A191122              where (m, s') = deleteFindMin s
%o A191122 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A191122 Cf. A191113.
%K A191122 nonn
%O A191122 1,2
%A A191122 _Clark Kimberling_, May 27 2011