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%I #29 Dec 03 2023 12:35:12
%S 1,120,5040,479001600,6402373705728000,121645100408832000,
%T 2432902008176640000,1124000727777607680000,
%U 15511210043330985984000000,304888344611713860501504000000
%N Factorials with a record number of zeros.
%H Michael De Vlieger, <a href="/A031145/b031145.txt">Table of n, a(n) for n = 0..59</a>
%e From _Alonso del Arte_, May 19 2017: (Start)
%e Note that 5040 has two zeros, even though only one of them is a trailing zero.
%e Although 3628800 has one more zero than 362880, it still has as many zeros as 5040, and for that reason it is not in this sequence.
%e Thus the next term after 5040 is 479001600, which has four zeros. (End)
%t Function[s, Map[Position[s, #][[1, 1]] &, Union@ FoldList[Max, s]]! ]@ Table[DigitCount[n!, 10, 0], {n, 28}] (* _Michael De Vlieger_, May 20 2017 *)
%t DeleteDuplicates[Table[{n!,DigitCount[n!,10,0]},{n,50}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Dec 03 2023 *)
%Y Cf. A031144 (indices of factorials), A027868.
%K nonn,base,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Erich Friedman_.
%E Name clarified by _Alonso del Arte_, May 19 2017
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