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

%I #6 Jan 08 2017 11:35:38

%S 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 66,69,73,77,81,85,89,93,97,101,105,109,113,117,121,125,129,133,137,

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

%C Sums of lengths of ternary numbers (A007089).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Ternary.html">Ternary</a>

%F G.f.: 1/(1 - x) + (1/(1 - x)^2)*Sum_{k>=0} x^(3^k).

%F a(n) = 1 + Sum_{k=1..n} floor(log_3(k)) + 1.

%e -----------------------

%e n base 3 length a(n)

%e -----------------------

%e 0 | 0 | 1 | 1

%e 1 | 1 | 1 | 2

%e 2 | 2 | 1 | 3

%e 3 | 10 | 2 | 5

%e 4 | 11 | 2 | 7

%e 5 | 12 | 2 | 9

%e 6 | 20 | 2 | 11

%e 7 | 21 | 2 | 13

%e 8 | 22 | 2 | 15

%e 9 | 100 | 3 | 18

%e -----------------------

%t CoefficientList[Series[1/(1 - x) + (1/(1 - x)^2) Sum[x^3^k, {k, 0, 15}], {x, 0, 70}], x]

%t Table[1 + Sum[Floor[Log[3, k]] + 1, {k, 1, n}], {n, 0, 70}]

%Y Cf. A007089, A062153, A081604, A083652, A117804.

%K nonn,base,easy

%O 0,2

%A _Ilya Gutkovskiy_, Jan 07 2017

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)