A277732 - OEIS

%I #16 Mar 20 2023 06:24:23

%S 1,3,6,8,11,12,14,17,19,22,23,25,27,30,32,35,36,38,41,43,46,47,49,51,

%T 54,56,59,61,64,65,67,70,72,75,76,78,80,83,85,88,89,91,94,96,99,100,

%U 102,104,107,109,112,114,117,118,120,123,125,128,129,131,134,136,139,140,142,144,147,149,152,153

%N Positions of 0's in A277731.

%C {A277732, A277733, A277734} forms a three-way partition of the positive integers, similar to {A003144, A003145, A003146}.

%H N. J. A. Sloane, <a href="/A277732/b277732.txt">Table of n, a(n) for n = 1..20000</a>

%p with(ListTools);

%p T:=proc(S) Flatten(subs( {0=[0,1], 1=[0,1,2], 2=[0]}, S)); end;

%p S:=[0];

%p for n from 1 to 14 do S:=T(S); od:

%p S; # A277731

%p p0:=[]: p1:=[]: p2:=[]:

%p for i from 1 to nops(S) do

%p j:=S[i];

%p if j=0 then p0:=[op(p0),i];

%p elif j=1 then p1:=[op(p1),i];

%p else p2:=[op(p2),i]; fi: od:

%p p0; # A277732

%p p1; # A277733

%p p2; # A277734

%t m = 1000; (* number of terms of A277731 *)

%t S[1] = {0};

%t S[n_] := S[n] = SubstitutionSystem[{0 -> {0, 1}, 1 -> {0, 1, 2}, 2 -> {0}}, S[n - 1]];

%t For[n = 2, True, n++, If[PadRight[S[n], m] == PadRight[S[n - 1], m], Print["n = ", n]; Break[]]];

%t A277731 = Take[S[n], m];

%t Position[A277731, 0] // Flatten (* _Jean-François Alcover_, Mar 20 2023 *)

%Y Cf. A052980, A277731, A277733, A277734.

%Y Cf. also A003144, A003145, A003146.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Nov 07 2016