A213854 Least m>0 such that m!*3^m >= n!.

1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 47, 48, 48, 49, 50

Offset: 1

Author

Clark Kimberling, Jul 17 2012

Keywords

• nonn
• easy

Examples

			a(6) = 4 because 3^3*3! < 6! <= 3^4*4!.
		

Links

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

Crossrefs

Cf. A094331, A213851.

Programs

Maple

A213854 := proc(n)
        for m from 1 do
                if (3^m)*m! >= n! then
                        return m;
                end if;
        end do:
end proc: # R. J. Mathar, Jul 18 2012

Mathematica

Table[m=1; While[n!>(3^m)*m!, m++]; m, {n,1,100}]
With[{tbl=Table[m! 3^m,{m,60}]},Table[Position[tbl,?(#>n!&),1,1],{n,70}]]//Flatten (* _Harvey P. Dale, Jun 08 2024 *)