A073850 Cumulative sum of initial digits of (n base 4).

0, 1, 3, 6, 7, 8, 9, 10, 12, 14, 16, 18, 21, 24, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 127, 128, 129, 130

Offset: 0

Author

Jonathan Vos Post, Aug 28 2005

Keywords

• base
• easy
• nonn

Examples

			    n in   init  cumulative
n  base 4   dgt     sum
-  ------  ----  ----------
0     0      0       0
1     1      1       1
2     2      2       3
3     3      3       6
4    10      1       7
5    11      1       8
		

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, A007090, A109453.

Programs

Magma

[0] cat [&+[Reverse(Intseq(k,4))[1]:k in [1..n]]:n in [1..70]]; // Marius A. Burtea, Dec 19 2019

Formula

a(n) = Sum_{i=0..n} A000030(A007090(n)).

a(n) = Sum_{i=0..n} first-digit(i base 4) where (i base 4) = A007090(i).