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A007320 Number of steps needed for juggler sequence (A094683) started at n to reach 1.

%I A007320 M4047 #42 Feb 16 2025 08:32:31
%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,
%T A007320 8,3,17,3,14,3,5,3,6,3,6,3,6,3,11,5,11,5,11,5,11,5,5,5,11,5,11,5,5,3,
%U A007320 5,3,11,3,14,3,5,3,8,3,8,3,19,3,8,3,10,8,8,8,11,8,10,8,11,8,11,8,11,8,8,8,11
%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 C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 232.
%D A007320 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007320 Giovanni Resta, <a href="/A007320/b007320.txt">Table of n, a(n) for n = 1..10000</a>
%H A007320 H. J. Smith, <a href="https://web.archive.org/web/20171111172551/http://www.reocities.com/hjsmithh/Juggler/JuggWhat.html">Juggler Sequence</a>
%H A007320 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JugglerSequence.html">Juggler Sequence</a>
%H A007320 Wikipedia, <a href="http://en.wikipedia.org/wiki/Juggler_sequence">Juggler sequence</a>
%H A007320 R. G. Wilson, V, <a href="/A007320/a007320.pdf">Letter to N. J. A. Sloane, Sep. 1992</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 A007320 := proc(n)
%p A007320     local a,ntrack;
%p A007320     a := 0 ;
%p A007320     ntrack := n ;
%p A007320     while ntrack > 1 do
%p A007320         ntrack := A094683(ntrack) ;
%p A007320         a := a+1 ;
%p A007320     end do:
%p A007320     return a;
%p A007320 end proc: # _R. J. Mathar_, Apr 19 2013
%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}] (* _Robert G. Wilson v_, Jun 10 2004 *)
%Y A007320 Cf. A007321, A094683, A094698, A094679, A093685, A094716.
%K A007320 nonn
%O A007320 1,3
%A A007320 _N. J. A. Sloane_, _Robert G. Wilson v_, _Mira Bernstein_
%E A007320 Corrected and extended by _Jason Earls_, Jun 09 2004