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A109804 Cumulative sum of initial digits of (n base 6).

%I A109804 #13 Dec 05 2020 18:02:27
%S A109804 0,1,3,6,10,15,16,17,18,19,20,21,23,25,27,29,31,33,36,39,42,45,48,51,
%T A109804 55,59,63,67,71,75,80,85,90,95,100,105,106,107,108,109,110,111,112,
%U A109804 113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131
%N A109804 Cumulative sum of initial digits of (n base 6).
%D A109804 A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 164-192.
%F A109804 n (base 6) = A007092(n) A007092(0)=0, A007092(n)=10* A007092(n/6) if n==0 (mod 6), A007092(n)= A007092(n-1)+1 otherwise. - _Benoit Cloitre_, Dec 22 2002
%F A109804 a(n) below is Sum_{i=0..n} first-digit{(i base 6)}.
%F A109804 a(n) = Sum_{i=1..n} floor(n / 6^floor(log_6(n))) where log_6(n) is the logarithm to base 6.
%F A109804 a(n+1) = a(n) + first-digit-of((n+1) (base 6)).
%e A109804   n  Base 6  Initial  Cumulative Sum
%e A109804   0     0       0           0
%e A109804   1     1       1           1
%e A109804   2     2       2           3
%e A109804   3     3       3           6
%e A109804   4     4       4          10
%e A109804   5     5       5          15
%t A109804 Accumulate[Table[First[IntegerDigits[n,6]],{n,0,70}]] (* _Harvey P. Dale_, Oct 07 2012 *)
%Y A109804 Cf. A000030, A007092, A109453, A339256 (first differences).
%K A109804 base,easy,nonn
%O A109804 0,3
%A A109804 _Jonathan Vos Post_, Aug 30 2005