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A191124 Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-1 and 4x+2 are in a.

%I A191124 #11 Feb 11 2025 18:07:25
%S A191124 1,2,5,6,10,14,17,22,26,29,41,42,50,58,65,70,77,86,90,106,118,122,125,
%T A191124 149,166,170,173,194,202,209,230,234,257,262,269,282,310,317,346,353,
%U A191124 362,365,374,426,446,474,490,497,502,509,518,581,598,605,626,666,682,689,694,701,770,778,785,806,810,838,845,922,929,938,950
%N A191124 Increasing sequence generated by these rules:  a(1)=1, and if x is in a then 3x-1 and 4x+2 are in a.
%C A191124 See A191113.
%H A191124 Reinhard Zumkeller, <a href="/A191124/b191124.txt">Table of n, a(n) for n = 1..10000</a>
%t A191124 h = 3; i = -1; j = 4; k = 2; f = 1; g = 9;
%t A191124 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191124 *)
%t A191124 b = (a + 1)/3; c = (a - 2)/4; r = Range[1, 1500];
%t A191124 d = Intersection[b, r] (* A191172 *)
%t A191124 e = Intersection[c, r] (* A191173 *)
%t A191124 f[m_]:=Flatten[{3#-1,4#+2}&/@m]; Take[Flatten[NestList[f,{1},10]]//Union,100] (* _Harvey P. Dale_, Feb 11 2025 *)
%o A191124 (Haskell)
%o A191124 import Data.Set (singleton, deleteFindMin, insert)
%o A191124 a191124 n = a191124_list !! (n-1)
%o A191124 a191124_list = f $ singleton 1
%o A191124    where f s = m : (f $ insert (3*m-1) $ insert (4*m+2) s')
%o A191124              where (m, s') = deleteFindMin s
%o A191124 -- _Reinhard Zumkeller_, Jun 01 2011
%Y A191124 Cf. A191113.
%K A191124 nonn
%O A191124 1,2
%A A191124 _Clark Kimberling_, May 27 2011