%I A007320 M4047
%S A007320 0,1,6,2,5,2,4,2,7,7,4,7,4,7,6,3,4,3,9,3,9,3,9,3,11,6,6,6,9,6,6,6,8,6,
               8,
%T A007320 3,17,3,14,3,5,3,6,3,6,3,6,3,11,5,11,5,11,5,11,5,5,5,11,5,11,5,5,3,5,3,
%U A007320 11,3,14,3,5,3,8,3,8,3,19,3,8,3,10,8,8,8,11,8,10,8,11,8,11,8,11,8,8,8,
               11
%N A007320 Number of steps needed for juggler sequence (A094683) started at n to 
               reach 1.
%C A007320 It is not known if every starting value eventually reaches 1.
%D A007320 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007320 C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, 
               p. 232.
%H A007320 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               JugglerSequence.html">Juggler Sequence</a>
%H A007320 H. J. Smith, <a href="http://harry-j-smith.com/hjsmithh/Juggler/JuggWhat.html">
               Juggler Sequence</a>
%e A007320 The trajectory of 1 is 3, 5, 11, 36, 6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
               1, 1, 1, 1, 1, 1, ... so a(3) = 6.
%p A007320 f:=proc(n) if n mod 2 = 0 then RETURN(floor(sqrt(n))) else RETURN(floor(n^(3/
               2))); fi; end; h:=proc(n) local i,j,t1; i:=0; j:=100; t1:=n; while 
               t1 <> 1 and i < j do t1:=f(t1); i:=i+1; od: RETURN(min(i,j)); end;
%t A007320 js[n_] := If[ EvenQ[n], Floor[ Sqrt[n]], Floor[ Sqrt[n^3]]]; f[n_] := 
               Length[ NestWhileList[js, n, # != 1 &]] - 1; Table[ f[n], {n, 99}] 
               (from Robert G. Wilson v Jun 10 2004)
%Y A007320 Cf. A007321, A094683, A094698, A094679, A093685, A094716.
%Y A007320 Sequence in context: A058160 A033939 A021020 this_sequence A007321 A062828 
               A124457
%Y A007320 Adjacent sequences: A007317 A007318 A007319 this_sequence A007321 A007322 
               A007323
%K A007320 nonn
%O A007320 1,3
%A A007320 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Mira Bernstein (mira(AT)math.berkeley.edu)
%E A007320 Corrected and extended by Jason Earls, Jun 09 2004