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A191134 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 A191134 #8 Jul 13 2013 12:04:10
%S A191134 1,3,4,10,11,13,15,31,34,39,40,43,46,51,59,94,103,118,121,123,130,135,
%T A191134 139,154,155,159,171,178,183,203,235,283,310,355,364,370,375,391,406,
%U A191134 411,418,463,466,471,478,483,491,514,519,535,539,550,555,610,615,619,635,683,706,711,731,811,850,931,939,1066,1093,1111,1126
%N A191134 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 A191134 See A101113/
%H A191134 Reinhard Zumkeller, <a href="/A191134/b191134.txt">Table of n, a(n) for n = 1..10000</a>
%t A191134 h = 3; i = 1; j = 4; k = -1; f = 1; g = 9;
%t A191134 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]   (* A191134 *)
%t A191134 b = (a - 1)/3; c = (a + 1)/4; r = Range[1, 1500];
%t A191134 d = Intersection[b, r] (* A191192 *)
%t A191134 e = Intersection[c, r] (* A191193 *)
%o A191134 (Haskell)
%o A191134 import Data.Set (singleton, deleteFindMin, insert)
%o A191134 a191134 n = a191134_list !! (n-1)
%o A191134 a191134_list = f $ singleton 1
%o A191134    where f s = m : (f $ insert (3*m+1) $ insert (4*m-1) s')
%o A191134              where (m, s') = deleteFindMin s
%o A191134 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A191134 Cf. A191113.
%K A191134 nonn
%O A191134 1,2
%A A191134 _Clark Kimberling_, May 28 2011