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A190811 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x+1 and 3x are in a.

%I A190811 #9 Jul 13 2013 12:04:09
%S A190811 1,3,7,9,15,19,21,27,31,39,43,45,55,57,63,79,81,87,91,93,111,115,117,
%T A190811 127,129,135,159,163,165,171,175,183,187,189,223,231,235,237,243,255,
%U A190811 259,261,271,273,279,319,327,331,333,343,345,351,367,375,379,381,387,405,447,463,471,475,477,487,489,495,511,513,519,523,525,543
%N A190811 Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 2x+1 and 3x are in a.
%C A190811 See A190803.
%H A190811 Reinhard Zumkeller, <a href="/A190811/b190811.txt">Table of n, a(n) for n = 1..10000</a>
%t A190811 h = 2; i = 1; j = 3; k = 0; f = 1; g = 9 ;
%t A190811 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190811 *)
%t A190811 b = (a - 1)/2; c = a/3; r = Range[1, 300];
%t A190811 d = Intersection[b, r] (* A002977 *)
%t A190811 e = Intersection[c, r] (* A190857 *)
%o A190811 (Haskell)
%o A190811 import Data.Set (singleton, deleteFindMin, insert)
%o A190811 a190811 n = a190811_list !! (n-1)
%o A190811 a190811_list = f $ singleton 1
%o A190811    where f s = m : (f $ insert (2*m+1) $ insert (3*m) s')
%o A190811              where (m, s') = deleteFindMin s
%o A190811 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A190811 Cf. A190803.
%K A190811 nonn
%O A190811 1,2
%A A190811 _Clark Kimberling_, May 20 2011