%I #7 Jul 25 2012 12:49:59
%S 1,1,2,4,5,7,9,12,14,16,19,21,24,27,29,32,35,38,41,44,48,51,54,57,61,
%T 64,68,71,75,78,82,85,89,93,96,100,104,107,111,115,119,123,127,131,
%U 135,139,143,147,151,155,159,163,167,171,175
%N Least m>0 such that (1+r)^m >= n!, where r = (1+sqrt(5))/2, the golden ratio.
%H Clark Kimberling, <a href="/A214051/b214051.txt">Table of n, a(n) for n = 1..1000</a>
%p A214051 := proc(n)
%p local r,m;
%p r := (1+sqrt(5))/2 ;
%p for m from 1 do
%p if floor((1+r)^m) >= n! then
%p return m ;
%p end if;
%p end do:
%p end proc: # _R. J. Mathar_, Jul 23 2012
%t r=GoldenRatio;
%t Table[m=1;While[n!>(1+r)^m,m++];m,{n,1,100}]
%Y Cf. A214050.
%K nonn,easy
%O 1,3
%A _Clark Kimberling_, Jul 18 2012