A031145 Factorials with a record number of zeros.

1, 120, 5040, 479001600, 6402373705728000, 121645100408832000, 2432902008176640000, 1124000727777607680000, 15511210043330985984000000, 304888344611713860501504000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Examples

			From _Alonso del Arte_, May 19 2017: (Start)
Note that 5040 has two zeros, even though only one of them is a trailing zero.
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.
Thus the next term after 5040 is 479001600, which has four zeros. (End)
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..59

Crossrefs

Cf. A031144 (indices of factorials), A027868.

Programs

Mathematica

Function[s, Map[Position[s, #][[1, 1]] &, Union@ FoldList[Max, s]]! ]@ Table[DigitCount[n!, 10, 0], {n, 28}] (* Michael De Vlieger, May 20 2017 *)
DeleteDuplicates[Table[{n!,DigitCount[n!,10,0]},{n,50}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Dec 03 2023 *)

Extensions

More terms from Erich Friedman.

Name clarified by Alonso del Arte, May 19 2017