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A137581 Number of inner zeros in decimal representation of n!.

%I A137581 #24 Jun 28 2023 08:18:36
%S A137581 0,0,0,0,0,0,0,1,1,0,0,0,2,2,0,1,1,1,2,3,3,3,4,1,2,3,2,3,4,1,2,0,3,1,
%T A137581 4,1,2,4,8,4,0,6,4,4,3,3,6,1,4,4,7,6,6,5,6,5,4,7,4,6,5,12,6,7,6,5,8,7,
%U A137581 10,6,4,9,7,19,7,7,6,14,7,11,8,8,9,11,8,16,8,7,8,14,7,8,8,11,16,10,14,4,13
%N A137581 Number of inner zeros in decimal representation of n!.
%H A137581 Robert G. Wilson v, <a href="/A137581/b137581.txt">Table of n, a(n) for n = 0..10000</a>.
%H A137581 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A137581 a(n) = A027869(n) - A027868(n);
%F A137581 a(A137582(n)) = 0.
%F A137581 a(n) = A055641(A004154(n)). - _Reinhard Zumkeller_, Apr 01 2015
%p A137581 A137581:= proc(n) uses StringTools;
%p A137581 CountCharacterOccurrences(TrimRight(SubstituteAll(
%p A137581     convert(n!,string),"0"," "))," ")
%p A137581 end proc; # _Robert Israel_, May 07 2012
%t A137581 f[n_] := f[n] = Block[{a = n!}, While[Mod[a, 10] == 0, a = a/10]; Count[ IntegerDigits@a, 0]]; Table[f@n, {n, 0, 98}] (* _Robert G. Wilson v_, Jan 28 2008 *)
%t A137581 Table[DigitCount[n!/10^IntegerExponent[n!,10],10,0],{n,0,100}] (* _Harvey P. Dale_, Apr 10 2023 *)
%o A137581 (Haskell)
%o A137581 a137581 = a055641 . a004154  -- _Reinhard Zumkeller_, Apr 01 2015
%Y A137581 Cf. A000142, A027869, A027868, A137582.
%Y A137581 Cf. A004154, A055641.
%K A137581 nonn,base
%O A137581 0,13
%A A137581 _Reinhard Zumkeller_, Jan 27 2008