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