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A073851 Cumulative sum of initial digits of (n base 5).

%I A073851 #17 Dec 05 2020 23:23:17
%S A073851 0,1,3,6,10,11,12,13,14,15,17,19,21,23,25,28,31,34,37,40,44,48,52,56,
%T A073851 60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,
%U A073851 83,84,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121
%N A073851 Cumulative sum of initial digits of (n base 5).
%H A073851 A. Cobham, <a href="https://doi.org/10.1007/BF01706087">Uniform Tag Sequences</a>, Mathematical Systems Theory, 6 (1972), 164-192.
%F A073851 a(n) = Sum_{i=0..n} A000030(A007091(n)).
%F A073851 a(n) = Sum_{i=0..n} first-digit(i base 4) where (i base 5) = A007091(i);
%F A073851 A007091(0)=0, A007091(i) = 10*A007091(i/5) if i == 0 (mod 5), A007091(i) = A007091(i-1) + 1 otherwise.
%F A073851 a(n) = Sum_{i=1..n} floor(n / 5^(floor(log_5(n)))).
%F A073851 a(n+1) = a(n) + first-digit-of((n+1) (base 5)).
%e A073851     n in   init  cumulative
%e A073851 n  base 5   dgt     sum
%e A073851 -  ------  ----  ----------
%e A073851 0     0      0       0
%e A073851 1     1      1       1
%e A073851 2     2      2       3
%e A073851 3     3      3       6
%e A073851 4     4      4      10
%e A073851 5    10      1      11
%o A073851 (PARI) a(n) = if (n, sum(k=1, n, digits(k, 5)[1]), 0); \\ _Michel Marcus_, Dec 13 2017
%Y A073851 Cf. A000030, A007091, A109453, A339255 (first differences).
%K A073851 base,easy,nonn
%O A073851 0,3
%A A073851 _Jonathan Vos Post_, Aug 28 2005