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%I #5 Oct 15 2013 22:32:25
%S 1,2,4,4,8,6,30,8,18,10,24,12,30,30,36,16,150,18,50,20,1320,22,
%T 43366048,24,26092,26,350,28,41678,30,234421146,32,2438232,34,114,36,
%U 5184,38,132,40,124026,42,150,150,160,150,934,48,1008,50,1084,52,12202,54,1240,56
%N Largest value in trajectory when 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}, peak=a[101]=234421146.
%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[Max[fe[w]], {w, 1, 150}]
%Y Cf. A007320, A094683, A094716, A094396-A094401.
%K nonn
%O 1,2
%A _Labos Elemer_, Jun 18 2004
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