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A073850
Cumulative sum of initial digits of (n base 4).
0
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
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
KEYWORD
base,easy,nonn
AUTHOR
Jonathan Vos Post, Aug 28 2005
STATUS
approved