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A033054 Numbers whose base-3 representation Sum_{i=0..m} d(i)*3^i has d(i)=1 for m-i odd.

%I A033054 #21 Jul 23 2025 05:45:20
%S A033054 1,2,4,7,12,13,14,21,22,23,37,40,43,64,67,70,111,112,113,120,121,122,
%T A033054 129,130,131,192,193,194,201,202,203,210,211,212,334,337,340,361,364,
%U A033054 367,388,391,394,577,580,583,604,607,610,631
%N A033054 Numbers whose base-3 representation Sum_{i=0..m} d(i)*3^i has d(i)=1 for m-i odd.
%H A033054 Robert Israel, <a href="/A033054/b033054.txt">Table of n, a(n) for n = 1..10000</a>
%F A033054 From _Robert Israel_, Jun 06 2016: (Start)
%F A033054 a(3n+3) = 9a(n)+4.
%F A033054 If A110654(n) is in A132141 then a(3n+2) = 9a(n)+3 and a(3n+4) = 9a(n)+5
%F A033054 otherwise a(3n+2) = 9a(n)+1 and a(3n+4) = 9a(n)+7.
%F A033054 G.f. satisfies g(x) = 9(x^2+x^3+x^4)g(x^3) + (x+2x^2+4x^3+6x^4-x^5)/(1-x^3) + ((2+2x)/(x+x^2+x^3)) Sum_{k>=1}(x^(2*3^k)-x^(4*3^k)).
%F A033054 (End)
%p A033054 N:= 1000: # to get a(1) to a(N)
%p A033054 K:= ceil((N-4)/3):
%p A033054 Dmax:= ilog[3](ceil(K/2+1)):
%p A033054 A:= Vector(3*K+4):
%p A033054 A[1..4]:= <1,2,4,7>:
%p A033054 for d from 0 to Dmax do
%p A033054   for k from 2*3^d-1 to min(4*3^d-2,K) do
%p A033054      A[3*k+2]:= 9*A[k]+3;
%p A033054      A[3*k+3]:= 9*A[k]+4;
%p A033054      A[3*k+4]:= 9*A[k]+5
%p A033054   od:
%p A033054   for k from 4*3^d-1 to min(2*3^(d+1)-2,K) do
%p A033054      A[3*k+2]:= 9*A[k]+1;
%p A033054      A[3*k+3]:= 9*A[k]+4;
%p A033054      A[3*k+4]:= 9*A[k]+7
%p A033054   od:
%p A033054 od:
%p A033054 seq(A[i],i=1..N); # _Robert Israel_, Jun 06 2016
%Y A033054 Disjoint with A032953 if more than 1 digit.
%K A033054 nonn,base
%O A033054 1,2
%A A033054 _Clark Kimberling_
%E A033054 Name corrected by _Robert Israel_, Jun 06 2016