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

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

Keywords

• nonn

Comments

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

Examples

			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.
		

References

• C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 232.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• H. J. Smith, Juggler Sequence
• Eric Weisstein's World of Mathematics, Juggler Sequence
• Wikipedia, Juggler sequence
• R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992

Crossrefs

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

Programs

Maple

A007320 := proc(n)
    local a,ntrack;
    a := 0 ;
    ntrack := n ;
    while ntrack > 1 do
        ntrack := A094683(ntrack) ;
        a := a+1 ;
    end do:
    return a;
end proc: # R. J. Mathar, Apr 19 2013

Mathematica

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 *)

Extensions

Corrected and extended by Jason Earls, Jun 09 2004