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

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

Offset

0,2

Comments

Sums of lengths of ternary numbers (A007089).

Links

Table of n, a(n) for n=0..70.

Eric Weisstein's World of Mathematics, Ternary

Formula

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

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

Example

-----------------------
n  base 3 length  a(n)
-----------------------
0 |  0   |  1   |  1
1 |  1   |  1   |  2
2 |  2   |  1   |  3
3 |  10  |  2   |  5
4 |  11  |  2   |  7
5 |  12  |  2   |  9
6 |  20  |  2   |  11
7 |  21  |  2   |  13
8 |  22  |  2   |  15
9 |  100 |  3   |  18
-----------------------

Mathematica

CoefficientList[Series[1/(1 - x) + (1/(1 - x)^2) Sum[x^3^k, {k, 0, 15}], {x, 0, 70}], x]
Table[1 + Sum[Floor[Log[3, k]] + 1, {k, 1, n}], {n, 0, 70}]

Crossrefs

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

Sequence in context: A054022 A185603 A046654 * A023543 A129895 A256212

Adjacent sequences: A280721 A280722 A280723 * A280725 A280726 A280727

Keyword

nonn,base,easy

Author

Ilya Gutkovskiy, Jan 07 2017

Status

approved