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A191109 a(1)=1, and if x is a term then 3x-1 and 3x+2 are terms too.

%I A191109 #15 Jul 29 2021 07:25:26
%S A191109 1,2,5,8,14,17,23,26,41,44,50,53,68,71,77,80,122,125,131,134,149,152,
%T A191109 158,161,203,206,212,215,230,233,239,242,365,368,374,377,392,395,401,
%U A191109 404,446,449,455,458,473,476,482,485,608,611,617,620,635,638,644,647,689,692,698,701,716,719,725,728,1094,1097,1103,1106,1121
%N A191109 a(1)=1, and if x is a term then 3x-1 and 3x+2 are terms too.
%C A191109 See discussions at A190803, A191106.
%C A191109 The positive integers in (1+A191109)/3 comprise A153775, a proper subsequence of A191109.
%C A191109 The positive integers in (-2+A191109)/3 comprise A032924, a proper subsequence of A191109.
%H A191109 Ivan Neretin, <a href="/A191109/b191109.txt">Table of n, a(n) for n = 1..10000</a>
%H A191109 Juha Honkala, <a href="http://www.acadsci.fi/mathematica/Vol14/vol14pp149-156.pdf">On number systems with negative digits</a>, Annales Academiae Scientiarum Fennicae, Series A. I. Mathematica, Vol. 14, 1989, pp. 149-156.
%t A191109 h = 3; i = -1; j = 3; k = 2; f = 1;  g = 7;
%t A191109 a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* 191109 *)
%t A191109 b = (a + 1)/3; c = (a - 2)/3; r = Range[1, 900];
%t A191109 d = Intersection[b, r] (* A153775 *)
%t A191109 e = Intersection[c, r] (* A032924 *)
%t A191109 Nest[Flatten[{#,3#-1,3#+2}]&,1,10]//Union (* _Harvey P. Dale_, Apr 05 2020 *)
%Y A191109 Cf. A190803, A191106, A153775, A032924.
%K A191109 nonn
%O A191109 1,2
%A A191109 _Clark Kimberling_, May 26 2011
%E A191109 Name edited by _Michel Marcus_, Jul 29 2021