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A073849
Cumulative sum of initial digits of (n base 3).
0
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
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
KEYWORD
easy,nonn,base
AUTHOR
Jonathan Vos Post, Aug 28 2005
EXTENSIONS
Corrected by Harvey P. Dale, Mar 24 2015
STATUS
approved