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

Author

Jonathan Vos Post, Aug 28 2005

Keywords

• easy
• nonn
• base

Examples

			    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
		

Links

• 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.

Crossrefs

Cf. A000030, A007089, A109453.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

Corrected by Harvey P. Dale, Mar 24 2015