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A230403 a(n) = the largest k such that (k+1)! divides n; the number of trailing zeros in the factorial base representation of n (A007623(n)). 12
0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Many of the comments given in A055881 apply also here.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10080

Tyler Ball, Joanne Beckford, Paul Dalenberg, Tom Edgar, Tina Rajabi, Some Combinatorics of Factorial Base Representations, J. Int. Seq., Vol. 23 (2020), Article 20.3.3.

FORMULA

a(n) = A055881(n)-1.

EXAMPLE

In factorial number base representation (A007623), the numbers from 1 to 9 are represented as:

n  A007623(n)  a(n) (gives the number of trailing zeros)

1        1       0

2       10       1

3       11       0

4       20       1

5       21       0

6      100       2

7      101       0

8      110       1

9      111       0

MATHEMATICA

With[{b = MixedRadix[Range[12, 2, -1]]}, Array[LengthWhile[Reverse@ IntegerDigits[#, b], # == 0 &] &, 105]] (* Michael De Vlieger, Jun 03 2020 *)

PROG

(Scheme)

(define (A230403 n) (if (zero? n) 0 (let loop ((n n) (i 2)) (cond ((not (zero? (modulo n i))) (- i 2)) (else (loop (/ n i) (1+ i)))))))

CROSSREFS

Cf. A055881. Bisection: A230404.

A few sequences related to factorial base representation (A007623): A034968, A084558, A099563, A060130, A227130, A227132, A227148, A227149, A153880.

Analogous sequence for binary system: A007814.

Sequence in context: A097796 A117188 A276084 * A248908 A133565 A239704

Adjacent sequences:  A230400 A230401 A230402 * A230404 A230405 A230406

KEYWORD

nonn,base,easy

AUTHOR

Antti Karttunen, Oct 31 2013

STATUS

approved

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Last modified July 3 23:36 EDT 2020. Contains 335419 sequences. (Running on oeis4.)