A033054 - OEIS

%I #17 Feb 15 2021 22:31:10

%S 1,2,4,7,12,13,14,21,22,23,37,40,43,64,67,70,111,112,113,120,121,122,

%T 129,130,131,192,193,194,201,202,203,210,211,212,334,337,340,361,364,

%U 367,388,391,394,577,580,583,604,607,610,631

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

%H Robert Israel, <a href="/A033054/b033054.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Robert Israel_, Jun 06 2016: (Start)

%F a(3n+3) = 9a(n)+4.

%F If A110654(n) is in A132141 then a(3n+2) = 9a(n)+3 and a(3n+4) = 9a(n)+5

%F otherwise a(3n+2) = 9a(n)+1 and a(3n+4) = 9a(n)+7.

%F 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 (End)

%p N:= 1000: # to get a(1) to a(N)

%p K:= ceil((N-4)/3):

%p Dmax:= ilog[3](ceil(K/2+1)):

%p A:= Vector(3*K+4):

%p A[1..4]:= <1,2,4,7>:

%p for d from 0 to Dmax do

%p   for k from 2*3^d-1 to min(4*3^d-2,K) do

%p      A[3*k+2]:= 9*A[k]+3;

%p      A[3*k+3]:= 9*A[k]+4;

%p      A[3*k+4]:= 9*A[k]+5

%p   od:

%p   for k from 4*3^d-1 to min(2*3^(d+1)-2,K) do

%p      A[3*k+2]:= 9*A[k]+1;

%p      A[3*k+3]:= 9*A[k]+4;

%p      A[3*k+4]:= 9*A[k]+7

%p   od:

%p od:

%p seq(A[i],i=1..N); # _Robert Israel_, Jun 06 2016

%K nonn,base

%O 1,2

%A _Clark Kimberling_

%E Name corrected by _Robert Israel_, Jun 06 2016