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A109804
Cumulative sum of initial digits of (n base 6).
1
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.
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 A375750 A120993
KEYWORD
base,easy,nonn
AUTHOR
Jonathan Vos Post, Aug 30 2005
STATUS
approved