A213854 -id:A213854 - cp's OEIS frontend

A213857 Least m such that n! <= 3^m.

1, 1, 2, 3, 5, 6, 8, 10, 12, 14, 16, 19, 21, 23, 26, 28, 31, 34, 36, 39, 42, 45, 47, 50, 53, 56, 59, 62, 65, 68, 72, 75, 78, 81, 84, 88, 91, 94, 98, 101, 104, 108, 111, 115, 118, 122, 125, 129, 132, 136, 139, 143, 146, 150, 154, 157, 161, 165, 168, 172, 176

Offset: 1

Clark Kimberling, Jul 17 2012

Also the number of digits in the ternary representation of n!. - Martin Renner, Jan 03 2022

			a(8) = 10 because 3^9 < 8! <= 3^10.

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

Cf. A003070, A072831, A213854.

seq(nops(convert(n!,base,3)),n=1..100); # Martin Renner, Jan 03 2022

Table[m=1; While[n!>3^m, m++]; m, {n,1,100}]

A213855 Least m > 0 such that m! * 4^m >= n!.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Jul 17 2012

			a(5) = 3 because (4^2)*2! < 5! <= (4^3)*3!.

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

Cf. A213854.

A213855 := proc(n)
        for m from 1 do
                if (4^m)*m! >= n! then
                        return m;
                end if;
        end do:
end proc: # R. J. Mathar, Jul 18 2012

Table[m=1; While[n!>(4^m)*m!, m++]; m, {n,1,100}]

cp's OEIS Frontend

A213857 Least m such that n! <= 3^m.

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