A007320 Number of steps needed for juggler sequence (A094683) started at n to reach 1. (Formerly M4047)

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

1,3

Comments

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

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A033939 A021020 A215578 * A199734 A007321 A062828

Adjacent sequences: A007317 A007318 A007319 * A007321 A007322 A007323

Keyword

nonn

Author

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

Extensions

Corrected and extended by Jason Earls, Jun 09 2004

Status

approved