%I #21 Dec 15 2017 17:36:39
%S 1,2,4,16,7,5,3,9,33,19,81,25,353,183,39,201,103,37,205,77,681,263,
%T 3817,429,175,1673,539,165,671,321,5875,477,173,2243,265,29017,1011,
%U 677,9361,659,241,3389,1123,163,2057,625,15271,4481
%N Smallest number which requires n iterations to reach 1 in the juggler sequence problem.
%C A juggler sequence is defined as follows: given a positive integer x, repeat: if x is even then x <- [x^(1/2)] else x <- [x^(3/2)] until x=1. The brackets indicate the floor function.
%C a(104) is unknown ( > 10000000). - _Robert G. Wilson v_, Jun 11 2014
%H Robert G. Wilson v, <a href="/A094670/b094670.txt">Table of n, a(n) for n = 0..103</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JugglerSequence.html">Juggler Sequence</a>
%H Robert G. Wilson v, <a href="/A094670/a094670.txt">List of n & a(n) for n = 0..450 (with 0's for unknown entries)</a>
%t js[n_] := If[ EvenQ[ n], Floor[ Sqrt[n]], Floor[ Sqrt[n^3]]]; f[n_] := Length[ NestWhileList[js, n, # != 1 &]] - 1; a = Table[0, {50}]; Do[ b = f[n]; If[b < 51 && a[[b]] == 0, a[[b]] = n; Print[n, " = ", b]], {n, 10^5}] (* _Robert G. Wilson v_ *)
%Y Cf. A007320, A094679, A094698.
%K nonn
%O 0,2
%A _Jason Earls_, Jun 09 2004
%E More terms from _Robert G. Wilson v_, Jun 14 2004