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A280724 Expansion of 1/(1 - x) + (1/(1 - x)^2)*Sum_{k>=0} x^(3^k). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Sums of lengths of ternary numbers (A007089).
LINKS
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
Sequence in context: A054022 A185603 A046654 * A023543 A129895 A256212
KEYWORD
nonn,base,easy
AUTHOR
Ilya Gutkovskiy, Jan 07 2017
STATUS
approved

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Last modified February 23 11:40 EST 2024. Contains 370283 sequences. (Running on oeis4.)