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A191610 Possible number of trailing zeros in n!. 6
0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 117, 118, 119, 120, 121, 124, 125, 126, 127, 128, 130, 131, 132, 133, 134, 136 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equivalently, possible values of 10-adic valuation of n!. - Joerg Arndt, Sep 21 2020

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) ~ 5*n/4. - Vaclav Kotesovec, Sep 21 2020

G.f.: 1/(1-x) * Sum_{k>=0} x^(5^k)/(1-x^5^k). - Joerg Arndt, Sep 21 2020

PROG

(Haskell)

a191610 1 = 0

a191610 n = sum $ takeWhile (> 0) $ map ((n - 1) `div`) a000351_list

-- Reinhard Zumkeller, Oct 31 2012

(Python)

# requires Python 3.2 and higher

from itertools import accumulate

from sympy import multiplicity

A191610 = [0]+list(accumulate(multiplicity(5, n) for n in range(5, 10**3, 5)))

# Chai Wah Wu, Sep 05 2014

CROSSREFS

Cf. A027868, A000351, A055457 (first differences).

Complement of A000966.

Sequence in context: A047226 A059537 A039259 * A037465 A157846 A285126

Adjacent sequences:  A191607 A191608 A191609 * A191611 A191612 A191613

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Jun 09 2011

STATUS

approved

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Last modified May 8 22:05 EDT 2021. Contains 343668 sequences. (Running on oeis4.)