%I
%S 1,1,2,3,3,4,4,5,5,6,7,7,8,9,11,9,10,11,11,11,13,13,14,13,14,15,17,17,
%T 18,19,18,23,19,21,22,22,23,22,25,29,23,26,25,27,26,27,29,31,30,29,28,
%U 33,33,31,34,41,32,36,33,37,33,35,37,39,47,37,41,42,40,41,41,53,45,43
%N Least k, 1<= k <=n, such that the number of elements of the continued fraction for n/k is maximum.
%C Also, for n > 1, the smallest number k such that the Euclidean algorithm for (n,k) requires the maximum number of steps, A034883(n).  _T. D. Noe_, Mar 24 2011
%F k>1, a(F(k))=F(k1) where F(k) denotes the kth Fibonacci number; probably, limit n >oo 1/n*sum(k=1, n, a(k)) = 1/phi where phi is the Golden ratio (1+sqrt(5))/2
%o (PARI) a(n)=if(n<0,0,s=1; while(abs(vecmax(vector(n,i,length(contfrac(n/i))))length(contfrac(n/s)))>0,s++); s)
%Y Cf. A071677.
%K nonn
%O 1,3
%A _Benoit Cloitre_, Jun 21 2003
