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A190805 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x-1 and 3x+1 are in a.

%I A190805 #12 Jul 13 2013 12:04:09
%S A190805 1,4,7,13,22,25,40,43,49,67,76,79,85,97,121,130,133,148,151,157,169,
%T A190805 193,202,229,238,241,256,259,265,292,295,301,313,337,364,385,391,400,
%U A190805 403,445,454,457,472,475,481,508,511,517,529,580,583,589,601,607,625,673,688,715,724,727
%N A190805 Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 2x-1 and 3x+1 are in a.
%C A190805 See A190803.
%H A190805 Reinhard Zumkeller, <a href="/A190805/b190805.txt">Table of n, a(n) for n = 1..10000</a>
%t A190805 h = 2; i = -1; j = 3; k = 1; f = 1; g = 10 ;
%t A190805 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190805 *)
%t A190805 b = (a + 1)/2; c = (a - 1)/3; r = Range[1, 500];
%t A190805 d = Intersection[b, r] (* A190845 *)
%t A190805 e = Intersection[c, r] (* A190808 conjectured *)
%o A190805 (Haskell)
%o A190805 import Data.Set (singleton, deleteFindMin, insert)
%o A190805 a190805 n = a190805_list !! (n-1)
%o A190805 a190805_list = 1 : f (singleton 4)
%o A190805    where f s = m : (f $ insert (2*m-1) $ insert (3*m+1) s')
%o A190805              where (m, s') = deleteFindMin s
%o A190805 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A190805 Cf. A190803, A190845.
%K A190805 nonn
%O A190805 1,2
%A A190805 _Clark Kimberling_, May 20 2011
%E A190805 a(56)=673 inserted by _Reinhard Zumkeller_, Jun 01 2011