login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A027869 Number of 0's in n!. 22

%I #55 Feb 11 2022 17:17:54

%S 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,

%T 8,11,9,10,12,16,12,9,15,13,13,12,13,16,11,14,14,19,18,18,17,18,18,17,

%U 20,17,19,19,26,20,21,20,20,23,22,25,21,20,25,23,35

%N Number of 0's in n!.

%H T. D. Noe, <a href="/A027869/b027869.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.

%F 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

%F A027868(n) <= a(n). - _Reinhard Zumkeller_, Jan 27 2008

%F 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

%t Table[Count[IntegerDigits[n!], 0], {n, 0, 100}] (* _T. D. Noe_, Apr 10 2012 *)

%t DigitCount[Range[0,80]!,10,0] (* _Harvey P. Dale_, Jul 08 2020 *)

%o (PARI) a(n)=my(d=digits(n!)); sum(i=1,#d,d[i]==0) \\ _Charles R Greathouse IV_, Jul 06 2017

%o (Python)

%o from math import factorial

%o def a(n): return str(factorial(n)).count('0')

%o print([a(n) for n in range(74)]) # _Michael S. Branicky_, Jan 11 2022

%Y Cf. A000142, A137579, A137580, A034886.

%K nonn,base

%O 0,8

%A _N. J. A. Sloane_

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)