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A190810 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 A190810 #12 Jul 14 2016 16:05:30
%S A190810 1,2,3,5,7,8,11,14,15,17,20,23,29,31,32,35,41,44,47,50,59,63,65,68,71,
%T A190810 83,86,89,92,95,101,104,119,122,127,131,137,140,143,149,167,173,176,
%U A190810 179,185,188,191,194,203,209,212,239,245,248,255,257,263,266,275,281
%N A190810 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 A190810 See A190803.
%H A190810 Reinhard Zumkeller, <a href="/A190810/b190810.txt">Table of n, a(n) for n = 1..10000</a>
%t A190810 h = 2; i = 1; j = 3; k = -1; f = 1; g = 9 ;
%t A190810 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A190810 *)
%t A190810 b = (a - 1)/2; c = (a + 1)/3; r = Range[1, 900];
%t A190810 d = Intersection[b, r] (* A190855 *)
%t A190810 e = Intersection[c, r] (* A190856 *)
%o A190810 (Haskell)
%o A190810 import Data.Set (singleton, deleteFindMin, insert)
%o A190810 a190810 n = a190810_list !! (n-1)
%o A190810 a190810_list = f $ singleton 1
%o A190810    where f s = m : (f $ insert (2*m+1) $ insert (3*m-1) s')
%o A190810              where (m, s') = deleteFindMin s
%o A190810 -- _Reinhard Zumkeller_, Jun 01 2011
%o A190810 (PARI) is(n)=if(n<7, n!=4, (n%3==1 && is(n\3)) || (n%2 && is(n\2))) \\ _Charles R Greathouse IV_, Jul 14 2016
%Y A190810 Cf. A190803, A190855, A190856.
%K A190810 nonn
%O A190810 1,2
%A A190810 _Clark Kimberling_, May 20 2011
%E A190810 a(55)=255 inserted by _Reinhard Zumkeller_, Jun 01 2011