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A191121 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 A191121 #9 Jul 13 2013 12:04:10
%S A191121 1,2,3,5,7,8,11,14,19,20,23,27,31,32,41,43,55,56,59,68,75,79,80,91,92,
%T A191121 95,107,122,123,127,128,163,164,167,171,176,203,219,223,224,235,236,
%U A191121 239,271,272,275,284,299,315,319,320,363,365,367,368,379,380,383,427,487,488,491,500,507,511,512,527,608,651,655,656,667,668
%N A191121 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 A191121 See A191113.
%H A191121 Reinhard Zumkeller, <a href="/A191121/b191121.txt">Table of n, a(n) for n = 1..10000</a>
%t A191121 h = 3; i = -1; j = 4; k = -1; f = 1; g = 9;
%t A191121 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191121 *)
%t A191121 b = (a + 1)/3; c = (a + 1)/4; r = Range[1, 1500];
%t A191121 d = Intersection[b, r] (* A191166 *)
%t A191121 e = Intersection[c, r] (* A191167 *)
%o A191121 (Haskell)
%o A191121 import Data.Set (singleton, deleteFindMin, insert)
%o A191121 a191121 n = a191121_list !! (n-1)
%o A191121 a191121_list = f $ singleton 1
%o A191121    where f s = m : (f $ insert (3*m-1) $ insert (4*m-1) s')
%o A191121              where (m, s') = deleteFindMin s
%o A191121 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A191121 Cf. A191113, A191166, A191167.
%K A191121 nonn
%O A191121 1,2
%A A191121 _Clark Kimberling_, May 27 2011