A031145 Factorials with a record number of zeros.

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

Offset

0,2

Links

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

Example

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)

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 *)

Crossrefs

Cf. A031144 (indices of factorials), A027868.

Sequence in context: A072419 A246193 A246613 * A126245 A221435 A229636

Adjacent sequences: A031142 A031143 A031144 * A031146 A031147 A031148

Keyword

nonn,base,easy

Author

N. J. A. Sloane.

Extensions

More terms from Erich Friedman.

Name clarified by Alonso del Arte, May 19 2017

Status

approved