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A190812 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 A190812 #10 Jul 13 2013 12:04:09
%S A190812 1,3,5,7,11,15,17,23,31,35,47,53,63,71,95,107,127,143,161,191,215,255,
%T A190812 287,323,383,431,485,511,575,647,767,863,971,1023,1151,1295,1457,1535,
%U A190812 1727,1943,2047,2303,2591,2915,3071,3455,3887,4095,4373,4607,5183,5831,6143,6911,7775,8191,8747,9215,10367,11663
%N A190812 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 A190812 See A190803.
%H A190812 Reinhard Zumkeller, <a href="/A190812/b190812.txt">Table of n, a(n) for n = 1..10000</a>
%t A190812 h = 2; i = 1; j = 3; k = 2; f = 1; g = 20 ;
%t A190812 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190812 *)
%t A190812 b = (a - 1)/2; c = (a - 2)/3; r = Range[1, 30000];
%t A190812 d = Intersection[b, r] (* A069353 *)
%t A190812 e = Intersection[c, r] (* A190812 conjectured *)
%o A190812 (Haskell)
%o A190812 import Data.Set (singleton, deleteFindMin, insert)
%o A190812 a190812 n = a190812_list !! (n-1)
%o A190812 a190812_list = f $ singleton 1
%o A190812    where f s = m : (f $ insert (2*m+1) $ insert (3*m+2) s')
%o A190812              where (m, s') = deleteFindMin s
%o A190812 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A190812 Cf. A190803, A069353, A190812.
%K A190812 nonn
%O A190812 1,2
%A A190812 _Clark Kimberling_, May 20 2011
%E A190812 a(41)=2047 inserted by _Reinhard Zumkeller_, Jun 01 2011