A073849 Cumulative sum of initial digits of (n base 3).

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

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