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

0, 1, 3, 6, 10, 11, 12, 13, 14, 15, 17, 19, 21, 23, 25, 28, 31, 34, 37, 40, 44, 48, 52, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121

Offset: 0

Author

Jonathan Vos Post, Aug 28 2005

Keywords

• base
• easy
• nonn

Examples

			    n in   init  cumulative
n  base 5   dgt     sum
-  ------  ----  ----------
0     0      0       0
1     1      1       1
2     2      2       3
3     3      3       6
4     4      4      10
5    10      1      11
		

Links

• A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 164-192.

Crossrefs

Cf. A000030, A007091, A109453, A339255 (first differences).

Programs

PARI

a(n) = if (n, sum(k=1, n, digits(k, 5)[1]), 0); \\ Michel Marcus, Dec 13 2017

Formula

a(n) = Sum_{i=0..n} A000030(A007091(n)).

a(n) = Sum_{i=0..n} first-digit(i base 4) where (i base 5) = A007091(i);

A007091(0)=0, A007091(i) = 10*A007091(i/5) if i == 0 (mod 5), A007091(i) = A007091(i-1) + 1 otherwise.

a(n) = Sum_{i=1..n} floor(n / 5^(floor(log_5(n)))).

a(n+1) = a(n) + first-digit-of((n+1) (base 5)).