A095401 - OEIS

%I #4 Oct 15 2013 22:32:25

%S 0,1,3,2,4,4,8,3,5,5,7,5,7,9,11,4,8,4,6,6,12,6,18,6,14,8,12,6,14,6,18,

%T 8,18,10,12,10,16,12,14,12,20,5,7,9,11,9,13,5,9,5,9,7,13,7,11,7,11,13,

%U 19,13,15,7,9,7,17,19,21,19,23,7,11,7,13,15,17,15,19,9,11,9,11,13,15,13,19

%N number of steps required to reach 1 if the following modified juggler map is iterated: a[n]=(1-Mod[n, 2])*Floor[n^(3/4)]+Mod[n, 2]*Floor[n^(4/3)]; original exponents {1/2, 3/2} are replaced with {3/4, 4/3}.

%e n=101: the trajectory is {101, 470, 100, 31, 97, 445, 3397, 51065, 1894513, 234421146, 1894512, 51064, 3396, 444, 96, 30, 12, 6, 3, 4, 2, 1}, number of required steps is a[101]=22-1=21.

%t e[x_]:=e[x]=(1-Mod[x, 2])*Floor[N[x^(3/4), 50]] +Mod[x, 2]*Floor[N[x^(4/3), 50]];e[1]=1; fe[x_]:=Delete[FixedPointList[e, x], -1]; Table[ -1+Length[fe[w]], {w, 1, 150}]

%Y Cf. A007320, A094683, A094716, A094396-A094400.

%K nonn

%O 1,3

%A _Labos Elemer_, Jun 18 2004