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A191114 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-2 and 4x-1 are in a.

%I A191114 #10 Jul 13 2013 12:04:09
%S A191114 1,3,7,11,19,27,31,43,55,75,79,91,107,123,127,163,171,219,223,235,271,
%T A191114 299,315,319,363,367,379,427,487,491,507,511,651,655,667,683,703,811,
%U A191114 875,891,895,939,943,955,1083,1087,1099,1135,1195,1259,1275,1279,1451,1459,1467,1471,1515,1519,1531,1707,1947,1951,1963,1999
%N A191114 Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 3x-2 and 4x-1 are in a.
%C A191114 See A191113.
%H A191114 Reinhard Zumkeller, <a href="/A191114/b191114.txt">Table of n, a(n) for n = 1..10000</a>
%t A191114 h = 3; i = -2; j = 4; k = -1; f = 1; g = 8;
%t A191114 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191114 *)
%t A191114 b = (a + 2)/3; c = (a + 1)/4; r = Range[1, 1200];
%t A191114 d = Intersection[b, r] (* A191121 *)
%t A191114 e = Intersection[c, r] (* A191152 *)
%t A191114 m = (a + 1)/2  (* divisibility property *)
%t A191114 p = (a + 1)/4  (* divisibility property *)
%o A191114 (Haskell)
%o A191114 import Data.Set (singleton, deleteFindMin, insert)
%o A191114 a191114 n = a191114_list !! (n-1)
%o A191114 a191114_list = 1 : f (singleton 3)
%o A191114    where f s = m : (f $ insert (3*m-2) $ insert (4*m-1) s')
%o A191114              where (m, s') = deleteFindMin s
%o A191114 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A191114 Cf. A191113.
%K A191114 nonn
%O A191114 1,2
%A A191114 _Clark Kimberling_, May 27 2011