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%I #17 Jun 27 2021 07:53:38
%S 0,1,0,4,3,1,0,13,12,10,9,4,3,1,0,40,39,37,36,31,30,28,27,13,12,10,9,
%T 4,3,1,0,121,120,118,117,112,111,109,108,94,93,91,90,85,84,82,81,40,
%U 39,37,36,31,30,28,27,13,12,10,9,4,3,1,0,364,363,361,360
%N G.f. 1/(1-x) * Sum_{k>=0} 3^k * x^2^(k+1)/(1+x^2^k).
%C Distance to next number of form 2^k-1, written down in binary, then interpreted as ternary. Thus the numbers have no 2 in ternary representation.
%H Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences with (relatively) simple ordinary generating functions</a>.
%H Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%F a(1)=0, a(2n) = 3a(n)+1, a(2n+1) = 3a(n).
%F a(n) = (1/2)*(3^(floor(log_2(n))+1)-1) - A005836(n).
%o (PARI) for(n=1, 100, l=ceil(log(n)/log(2)); t=polcoeff(1/(1-x)*sum(k=0, l, 3^k*(x^2^(k+1))/(1+x^2^k)) + O(x^(n+1)), n); print1(t", "))
%Y Cf. A005823, A005836.
%K nonn,easy
%O 1,4
%A _Ralf Stephan_, Jun 18 2003
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