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A084242 Least k, 1<= k <=n, such that the number of elements of the continued fraction for n/k is maximum. 6

%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(k-1) where F(k) denotes the k-th 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

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Last modified October 28 17:59 EDT 2021. Contains 348329 sequences. (Running on oeis4.)