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A073849 Cumulative sum of initial digits of (n base 3). 0
0, 1, 3, 4, 5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..66.

Hsien-Kuei Hwang, S. Janson, T.-H. Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint 2016.

Hsien-Kuei Hwang, S. Janson, T.-H. Tsai, Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585.

FORMULA

a(n) = Sum_{i=0..n} A000030(A007089(n)).

EXAMPLE

    n in   init  cumulative

n  base 3   dgt     sum

-  ------  ----  ----------

0     0      0       0

1     1      1       1

2     2      2       3

3    10      1       4

4    11      1       5

5    12      1       6

MATHEMATICA

Accumulate[Table[First[IntegerDigits[n, 3]], {n, 0, 80}]] (* Harvey P. Dale, Mar 24 2015 *)

PROG

(PARI) lista(nn) = {s = 0; print1(s, ", "); for (n=1, nn, s += digits(n, 3)[1]; print1(s, ", "); ); } \\ Michel Marcus, Mar 24 2015

CROSSREFS

Cf. A000030, A007089, A109453.

Sequence in context: A288041 A163406 A092253 * A288597 A297997 A136497

Adjacent sequences:  A073846 A073847 A073848 * A073850 A073851 A073852

KEYWORD

easy,nonn,base

AUTHOR

Jonathan Vos Post, Aug 28 2005

EXTENSIONS

Corrected by Harvey P. Dale, Mar 24 2015

STATUS

approved

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Last modified May 30 13:58 EDT 2020. Contains 334724 sequences. (Running on oeis4.)