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Search: id:A007320
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| A007320 |
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Number of steps needed for juggler sequence (A094683) started at n to reach 1.
(Formerly M4047)
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+0
18
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| 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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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It is not known if every starting value eventually reaches 1.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 232.
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LINKS
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Eric Weisstein's World of Mathematics, Juggler Sequence
H. J. Smith, Juggler Sequence
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EXAMPLE
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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.
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MAPLE
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f:=proc(n) if n mod 2 = 0 then RETURN(floor(sqrt(n))) else RETURN(floor(n^(3/2))); fi; end; h:=proc(n) local i, j, t1; i:=0; j:=100; t1:=n; while t1 <> 1 and i < j do t1:=f(t1); i:=i+1; od: RETURN(min(i, j)); end;
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MATHEMATICA
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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)
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CROSSREFS
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Cf. A007321, A094683, A094698, A094679, A093685, A094716.
Sequence in context: A058160 A033939 A021020 this_sequence A007321 A062828 A124457
Adjacent sequences: A007317 A007318 A007319 this_sequence A007321 A007322 A007323
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), Mira Bernstein (mira(AT)math.berkeley.edu)
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EXTENSIONS
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Corrected and extended by Jason Earls, Jun 09 2004
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