A213856 Least m such that m!*5^m >= n!.

1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 23, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 42, 42, 43, 44, 45, 45, 46

Offset: 1

Author

Clark Kimberling, Jul 17 2012

Keywords

• nonn
• easy

Examples

			a(6) = 3 because (5^2)*2! < 6! <= (5^3)*3!.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A213855.

Programs

Mathematica

Table[m=1; While[n!>(5^m)*m!, m++]; m, {n,1,100}]
Module[{nn=70,m},mt=Table[{m,m! 5^m},{m,nn}];Table[SelectFirst[mt,#[[2]] >= n!&],{n,nn}]][[All,1]] (* Harvey P. Dale, Sep 23 2018 *)