A339255 -id:A339255 - cp's OEIS frontend

A339256 Leading digit of n in base 6.

1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Kevin Ryde, Nov 28 2020

Kevin Ryde, Table of n, a(n) for n = 1..10000

Cf. A007092 (base 6), A109804 (partial sums).

In other bases: A122586, A122587, A339255, A000030, A099563, A276153.

Table[IntegerDigits[n,6][[1]],{n,90}] (* Harvey P. Dale, Jul 19 2023 *)

PARI
```
a(n) = n\6^logint(n,6);
```

a(n) = floor(n / 6^floor(log_6(n))).

G.f.: (x + Sum_{k>=0} Sum_{d=2..5} (x^(d*6^k)-x^(6^(k+1))) )/(1-x).

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

Original entry on oeis.org

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

Jonathan Vos Post, Aug 28 2005

			    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

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

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

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

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)).

cp's OEIS Frontend

A339256 Leading digit of n in base 6.

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