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A109804 Cumulative sum of initial digits of (n base 6). 0
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 (list; graph; refs; listen; history; text; internal format)
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, A109453.

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

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Last modified October 14 09:25 EDT 2019. Contains 327995 sequences. (Running on oeis4.)