A081111 - OEIS

A081111

Let s(x)=floor(phi*x) where phi is the golden ratio (1+sqrt(5))/2; sequence gives the least k such that n divides s^k(n) where s^k(x) denotes s(s(s..s(x))..) k times, or 0 if no such number exists.

%I #6 Mar 30 2012 18:39:16

%S 1,2,2,6,4,6,16,4,5,3,10,3,6,3,6,3,6,8,6,13,6,20,14,24,7,16,58,26,14,

%T 16,30,33,40,8,49,18,49,18,40,37,8,32,28,24,33,18,32,8,27,61,64,22,65,

%U 30,8,36,72,14,58,51,23,30,16,11,41,10,9,30,30,32,37,16,35,59,83,18,70,64,64

%N Let s(x)=floor(phi*x) where phi is the golden ratio (1+sqrt(5))/2; sequence gives the least k such that n divides s^k(n) where s^k(x) denotes s(s(s..s(x))..) k times, or 0 if no such number exists.

%e s(4)=6, s(s(4))=9, s(s(s(4)))=14, s(s(s(s(4))))=22, s(s(s(s(s(4)))))=35, s(s(s(s(s(s(4))))))=56 and 56=s^6(4) is divisible by 4. Hence a(4)=6.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Apr 15 2003