A191107 - OEIS

%I #35 Aug 14 2023 08:28:19

%S 1,4,10,13,28,31,37,40,82,85,91,94,109,112,118,121,244,247,253,256,

%T 271,274,280,283,325,328,334,337,352,355,361,364,730,733,739,742,757,

%U 760,766,769,811,814,820,823,838,841,847,850,973,976,982,985,1000,1003,1009,1012,1054,1057,1063,1066,1081,1084,1090,1093,2188

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

%C For general discussions, see A190803 and A191106.

%C Numbers whose base-3 representation ends in 1 and contains no 2; primitive members of A005836. - _Peter Munn_, Aug 14 2023

%H Robert Israel, <a href="/A191107/b191107.txt">Table of n, a(n) for n = 1..10000</a>

%H Barry Brent, <a href="https://doi.org/10.20944/preprints202306.1164.v6">On the Constant Terms of Certain Laurent Series</a>, Preprints (2023) 2023061164.

%F Conjecture: a(n) = 3*A003278(n) - 2 = (A055246(n) + 1)/2. - _L. Edson Jeffery_, Nov 25 2015

%F Conjecture: a(n) = A190640(n)/2. - _Michel Marcus_, Aug 24 2016

%F Conjecture: a(n) = A003278(2n-1). - _Arie Bos_, Aug 07 2022

%p N:= 100000: # to get all terms <= N

%p with(queue):

%p Q:= new(1):

%p A:= {}:

%p while not empty(Q) do

%p   s:= dequeue(Q);

%p   A:= A union {s};

%p   for t in {3*s-2,3*s+1} minus A do

%p     if t <= N then enqueue(Q,t) fi

%p   od

%p od:

%p sort(convert(A,list)); # _Robert Israel_, Nov 29 2015

%t h = 3; i = -2; j = 3; k = 1; f = 1;  g = 7;

%t a = Union[Flatten[NestList[{h # + i, j # + k} &, f, g]]]  (* A191107 *)

%t b = (a + 2)/3; c = (a - 1)/3; r = Range[1, 900];

%t d = Intersection[b, r] (* A003278 *)

%t e = Intersection[c, r] (* A005836 *)

%Y Cf. A003278, A005836, A055246, A190640, A190803, A191106.

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_, May 26 2011