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A027869 Number of 0's in n!. 22
0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 2, 2, 4, 4, 2, 4, 4, 4, 5, 6, 7, 7, 8, 5, 6, 9, 8, 9, 10, 7, 9, 7, 10, 8, 11, 9, 10, 12, 16, 12, 9, 15, 13, 13, 12, 13, 16, 11, 14, 14, 19, 18, 18, 17, 18, 18, 17, 20, 17, 19, 19, 26, 20, 21, 20, 20, 23, 22, 25, 21, 20, 25, 23, 35 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
LINKS
FORMULA
a(n) = A034886(n) - (A079680(n) + A079714(n) + A079684(n) + A079688(n) + A079690(n) + A079691(n) + A079692(n) + A079693(n) + A079694(n)). - Reinhard Zumkeller, Jan 27 2008
A027868(n) <= a(n). - Reinhard Zumkeller, Jan 27 2008
Conjecture: a(n) ~ (9*A027868(n) + A034886(n))/10. This formula is based on the assumption that the digits other than trailing zeros are uniformly randomly distributed. - Nicolas Bělohoubek, Jan 11 2022
MATHEMATICA
Table[Count[IntegerDigits[n!], 0], {n, 0, 100}] (* T. D. Noe, Apr 10 2012 *)
DigitCount[Range[0, 80]!, 10, 0] (* Harvey P. Dale, Jul 08 2020 *)
PROG
(PARI) a(n)=my(d=digits(n!)); sum(i=1, #d, d[i]==0) \\ Charles R Greathouse IV, Jul 06 2017
(Python)
from math import factorial
def a(n): return str(factorial(n)).count('0')
print([a(n) for n in range(74)]) # Michael S. Branicky, Jan 11 2022
CROSSREFS
Sequence in context: A334590 A115034 A253193 * A156748 A351455 A075445
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)