A073849 - OEIS

%I #29 Dec 18 2019 02:06:00

%S 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,

%T 37,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,

%U 61,62,63,64,65,66,68,70,72,74,76,78,80,82,84,86,88,90,92

%N Cumulative sum of initial digits of (n base 3).

%H Hsien-Kuei Hwang, S. Janson, T.-H. Tsai, <a href="http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf">Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications</a>, Preprint 2016.

%H Hsien-Kuei Hwang, S. Janson, T.-H. Tsai, <a href="https://doi.org/10.1145/3127585">Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications</a>, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585.

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

%e     n in   init  cumulative

%e n  base 3   dgt     sum

%e -  ------  ----  ----------

%e 0     0      0       0

%e 1     1      1       1

%e 2     2      2       3

%e 3    10      1       4

%e 4    11      1       5

%e 5    12      1       6

%t Accumulate[Table[First[IntegerDigits[n,3]],{n,0,80}]] (* _Harvey P. Dale_, Mar 24 2015 *)

%o (PARI) lista(nn) = {s = 0; print1(s, ", "); for (n=1, nn, s += digits(n,3)[1]; print1(s, ", "););} \\ _Michel Marcus_, Mar 24 2015

%Y Cf. A000030, A007089, A109453.

%K easy,nonn,base

%O 0,3

%A _Jonathan Vos Post_, Aug 28 2005

%E Corrected by _Harvey P. Dale_, Mar 24 2015