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

0,3

Links

Table of n, a(n) for n=0..67.

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

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)).

Example

    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

Prog

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

Crossrefs

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

Sequence in context: A135738 A307574 A169911 * A290541 A043321 A241858

Adjacent sequences: A073848 A073849 A073850 * A073852 A073853 A073854

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Aug 28 2005

Status

approved