A339256 -id:A339256 - cp's OEIS frontend

A339255 Leading digit of n in base 5.

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

Offset: 1

Kevin Ryde, Nov 28 2020

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

Cf. A007091 (base 5), A073851 (partial sums).

In other bases: A122586, A122587, A339256, A000030, A099563, A276153.

IntegerDigits[#,5][[1]]&/@Range[100] (* Harvey P. Dale, Sep 04 2021 *)

PARI
```
a(n) = n\5^logint(n,5);
```

a(n) = floor(n / 5^floor(log_5(n))).

G.f.: (x + Sum_{k>=0} Sum_{d=2..4} (x^(d*5^k)-x^(5^(k+1))) )/(1-x).

A109804 Cumulative sum of initial digits of (n base 6).

Original entry on oeis.org

0, 1, 3, 6, 10, 15, 16, 17, 18, 19, 20, 21, 23, 25, 27, 29, 31, 33, 36, 39, 42, 45, 48, 51, 55, 59, 63, 67, 71, 75, 80, 85, 90, 95, 100, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131

Offset: 0

Jonathan Vos Post, Aug 30 2005

			  n  Base 6  Initial  Cumulative Sum
  0     0       0           0
  1     1       1           1
  2     2       2           3
  3     3       3           6
  4     4       4          10
  5     5       5          15

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

Cf. A000030, A007092, A109453, A339256 (first differences).

Accumulate[Table[First[IntegerDigits[n,6]],{n,0,70}]] (* Harvey P. Dale, Oct 07 2012 *)

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
a(n) below is Sum_{i=0..n} first-digit{(i base 6)}.
a(n) = Sum_{i=1..n} floor(n / 6^floor(log_6(n))) where log_6(n) is the logarithm to base 6.
a(n+1) = a(n) + first-digit-of((n+1) (base 6)).

cp's OEIS Frontend

A339255 Leading digit of n in base 5.

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