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A190806 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x-1 and 3x+2 are in a.

%I A190806 #11 Jul 13 2013 12:04:09
%S A190806 1,5,9,17,29,33,53,57,65,89,101,105,113,129,161,173,177,197,201,209,
%T A190806 225,257,269,305,317,321,341,345,353,389,393,401,417,449,485,513,521,
%U A190806 533,537,593,605,609,629,633,641,677,681,689,705,773,777,785,801,809,833,897,917,953,965,969
%N A190806 Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 2x-1 and 3x+2 are in a.
%C A190806 See A190803.
%H A190806 Reinhard Zumkeller, <a href="/A190806/b190806.txt">Table of n, a(n) for n = 1..10000</a>
%t A190806 h = 2; i = -1; j = 3; k = 2; f = 1; g = 12 ;
%t A190806 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190806 *)
%t A190806 b = (a + 1)/2; c = (a - 2)/3; r = Range[1, 1200];
%t A190806 d = Intersection[b, r] (* A190804 conjectured *)
%t A190806 e = Intersection[c, r] (* A190848 *)
%o A190806 (Haskell)
%o A190806 import Data.Set (singleton, deleteFindMin, insert)
%o A190806 a190806 n = a190806_list !! (n-1)
%o A190806 a190806_list = 1 : f (singleton 5)
%o A190806    where f s = m : (f $ insert (2*m-1) $ insert (3*m+2) s')
%o A190806              where (m, s') = deleteFindMin s
%o A190806 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A190806 Cf. A190803, A190848.
%K A190806 nonn
%O A190806 1,2
%A A190806 _Clark Kimberling_, May 20 2011
%E A190806 a(56)=897 inserted by _Reinhard Zumkeller_, Jun 01 2011