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A191120 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-1 and 4x-2 are in a.

%I A191120 #11 Jul 13 2013 12:04:09
%S A191120 1,2,5,6,14,17,18,22,41,50,53,54,65,66,70,86,122,149,158,161,162,194,
%T A191120 197,198,209,210,214,257,258,262,278,342,365,446,473,482,485,486,581,
%U A191120 590,593,594,626,629,630,641,642,646,770,773,774,785,786,790,833,834,838,854,1025,1026,1030,1046,1094,1110,1337,1366,1418,1445
%N A191120 Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 3x-1 and 4x-2 are in a.
%C A191120 See A191113.
%H A191120 Reinhard Zumkeller, <a href="/A191120/b191120.txt">Table of n, a(n) for n = 1..10000</a>
%t A191120 h = 3; i = -1; j = 4; k = -2; f = 1; g = 9;
%t A191120 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191120 *)
%t A191120 b = (a + 1)/3; c = (a + 2)/4; r = Range[1, 1500];
%t A191120 d = Intersection[b, r] (* A191229 *)
%t A191120 e = Intersection[c, r] (* A191165 *)
%o A191120 (Haskell)
%o A191120 import Data.Set (singleton, deleteFindMin, insert)
%o A191120 a191120 n = a191120_list !! (n-1)
%o A191120 a191120_list = f $ singleton 1
%o A191120    where f s = m : (f $ insert (3*m-1) $ insert (4*m-2) s')
%o A191120              where (m, s') = deleteFindMin s
%o A191120 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A191120 Cf. A191113, A191229, A191165.
%K A191120 nonn
%O A191120 1,2
%A A191120 _Clark Kimberling_, May 27 2011