

A007320


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


18



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
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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

Table of n, a(n) for n=1..97.
H. J. Smith, Juggler Sequence [Broken link?]
Eric Weisstein's World of Mathematics, Juggler Sequence
Wikipedia, Juggler sequence


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}] (from 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



