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A280724 Expansion of 1/(1 - x) + (1/(1 - x)^2)*Sum_{k>=0} x^(3^k).

%I A280724 #7 Feb 16 2025 08:33:39
%S A280724 1,2,3,5,7,9,11,13,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,
%T A280724 66,69,73,77,81,85,89,93,97,101,105,109,113,117,121,125,129,133,137,
%U A280724 141,145,149,153,157,161,165,169,173,177,181,185,189,193,197,201,205,209,213,217,221,225,229,233,237,241,245
%N A280724 Expansion of 1/(1 - x) + (1/(1 - x)^2)*Sum_{k>=0} x^(3^k).
%C A280724 Sums of lengths of ternary numbers (A007089).
%H A280724 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ternary.html">Ternary</a>
%F A280724 G.f.: 1/(1 - x) + (1/(1 - x)^2)*Sum_{k>=0} x^(3^k).
%F A280724 a(n) = 1 + Sum_{k=1..n} floor(log_3(k)) + 1.
%e A280724 -----------------------
%e A280724 n  base 3 length  a(n)
%e A280724 -----------------------
%e A280724 0 |  0   |  1   |  1
%e A280724 1 |  1   |  1   |  2
%e A280724 2 |  2   |  1   |  3
%e A280724 3 |  10  |  2   |  5
%e A280724 4 |  11  |  2   |  7
%e A280724 5 |  12  |  2   |  9
%e A280724 6 |  20  |  2   |  11
%e A280724 7 |  21  |  2   |  13
%e A280724 8 |  22  |  2   |  15
%e A280724 9 |  100 |  3   |  18
%e A280724 -----------------------
%t A280724 CoefficientList[Series[1/(1 - x) + (1/(1 - x)^2) Sum[x^3^k, {k, 0, 15}], {x, 0, 70}], x]
%t A280724 Table[1 + Sum[Floor[Log[3, k]] + 1, {k, 1, n}], {n, 0, 70}]
%Y A280724 Cf. A007089, A062153, A081604, A083652, A117804.
%K A280724 nonn,base,easy
%O A280724 0,2
%A A280724 _Ilya Gutkovskiy_, Jan 07 2017