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

0,3

References

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

Links

Table of n, a(n) for n=0..61.

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)).

Example

  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

Mathematica

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

Crossrefs

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

Sequence in context: A259604 A130484 A074374 * A231672 A120993 A194458

Adjacent sequences: A109801 A109802 A109803 * A109805 A109806 A109807

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Aug 30 2005

Status

approved