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

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

Author

Jonathan Vos Post, Aug 30 2005

Keywords

• base
• easy
• nonn

Examples

			  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
		

References

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

Crossrefs

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

Programs

Mathematica

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

Formula

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)).