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A191116 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 A191116 #10 Jul 13 2013 12:04:09
%S A191116 1,5,13,21,37,53,61,85,109,149,157,181,213,245,253,325,341,437,445,
%T A191116 469,541,597,629,637,725,733,757,853,973,981,1013,1021,1301,1309,1333,
%U A191116 1365,1405,1621,1749,1781,1789,1877,1885,1909,2165,2173,2197,2269,2389,2517,2549,2557,2901,2917,2933,2941,3029,3037,3061,3413
%N A191116 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 A191116 See A191113.
%H A191116 Reinhard Zumkeller, <a href="/A191116/b191116.txt">Table of n, a(n) for n = 1..10000</a>
%t A191116 h = 3; i = -2; j = 4; k = 1; f = 1; g = 9;
%t A191116 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191116 *)
%t A191116 b = (a + 2)/3; c = (a - 1)/4; r = Range[1, 1500];
%t A191116 d = Intersection[b, r] (* A191155 *)
%t A191116 e = Intersection[c, r] (* A191129 *)
%t A191116 m = (a + 1)/2  (* divisibility property *)
%t A191116 p = (a + 3)/4  (* divisibility property *)
%t A191116 q = (a + 3)/8  (* divisibility property *)
%o A191116 (Haskell)
%o A191116 import Data.Set (singleton, deleteFindMin, insert)
%o A191116 a191116 n = a191116_list !! (n-1)
%o A191116 a191116_list = 1 : f (singleton 5)
%o A191116    where f s = m : (f $ insert (3*m-2) $ insert (4*m+1) s')
%o A191116              where (m, s') = deleteFindMin s
%o A191116 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A191116 Cf. A191113.
%K A191116 nonn
%O A191116 1,2
%A A191116 _Clark Kimberling_, May 27 2011