A007320 - OEIS

%I M4047 #42 Feb 16 2025 08:32:31

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

%C It is not known if every starting value eventually reaches 1.

%D C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 232.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Giovanni Resta, <a href="/A007320/b007320.txt">Table of n, a(n) for n = 1..10000</a>

%H H. J. Smith, <a href="https://web.archive.org/web/20171111172551/http://www.reocities.com/hjsmithh/Juggler/JuggWhat.html">Juggler Sequence</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JugglerSequence.html">Juggler Sequence</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Juggler_sequence">Juggler sequence</a>

%H R. G. Wilson, V, <a href="/A007320/a007320.pdf">Letter to N. J. A. Sloane, Sep. 1992</a>

%e 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 := proc(n)

%p     local a,ntrack;

%p     a := 0 ;

%p     ntrack := n ;

%p     while ntrack > 1 do

%p         ntrack := A094683(ntrack) ;

%p         a := a+1 ;

%p     end do:

%p     return a;

%p end proc: # _R. J. Mathar_, Apr 19 2013

%t 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 Cf. A007321, A094683, A094698, A094679, A093685, A094716.

%K nonn,changed

%O 1,3

%A _N. J. A. Sloane_, _Robert G. Wilson v_, _Mira Bernstein_

%E Corrected and extended by _Jason Earls_, Jun 09 2004