cp's OEIS Frontend

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

%I A213854 #11 Jun 08 2024 15:56:43
%S A213854 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,
%T A213854 21,22,23,24,25,25,26,27,28,29,29,30,31,32,33,34,34,35,36,37,38,38,39,
%U A213854 40,41,42,43,43,44,45,46,47,48,48,49,50
%N A213854 Least m>0 such that m!*3^m >= n!.
%H A213854 Clark Kimberling, <a href="/A213854/b213854.txt">Table of n, a(n) for n = 1..1000</a>
%e A213854 a(6) = 4 because 3^3*3! < 6! <= 3^4*4!.
%p A213854 A213854 := proc(n)
%p A213854         for m from 1 do
%p A213854                 if (3^m)*m! >= n! then
%p A213854                         return m;
%p A213854                 end if;
%p A213854         end do:
%p A213854 end proc: # _R. J. Mathar_, Jul 18 2012
%t A213854 Table[m=1; While[n!>(3^m)*m!, m++]; m, {n,1,100}]
%t A213854 With[{tbl=Table[m! 3^m,{m,60}]},Table[Position[tbl,_?(#>n!&),1,1],{n,70}]]//Flatten (* _Harvey P. Dale_, Jun 08 2024 *)
%Y A213854 Cf. A094331, A213851.
%K A213854 nonn,easy
%O A213854 1,3
%A A213854 _Clark Kimberling_, Jul 17 2012