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

0,3

Links

Table of n, a(n) for n=0..67.

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(A007090(n)).

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

Example

    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

Prog

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

Crossrefs

Cf. A000030, A007090, A109453.

Sequence in context: A068985 A081391 A296484 * A048748 A030781 A073417

Adjacent sequences: A073847 A073848 A073849 * A073851 A073852 A073853

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Aug 28 2005

Status

approved