A007321 Number of steps needed for modified juggler sequence (A094685) started at n to reach 1. (Formerly M4048)

0, 1, 6, 2, 5, 2, 13, 7, 10, 7, 4, 7, 6, 3, 9, 3, 9, 3, 12, 3, 9, 6, 9, 6, 19, 6, 9, 6, 9, 6, 16, 3, 5, 3, 8, 3, 16, 3, 5, 3, 14, 3, 11, 14, 11, 14, 5, 14, 14, 14, 14, 14, 5, 14, 5, 14, 11, 8, 11, 8, 8, 8, 8, 8, 11, 8, 11, 8, 8, 8, 8, 8, 21, 11, 21, 11, 8, 11, 8, 11, 19, 11, 11, 11, 8, 11, 11, 11, 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. 233.

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

Links

Richard J Mathar and Chai Wah Wu, Table of n, a(n) for n = 1..10000 n = 1..836 from Richard J Mathar

H. J. Smith, Juggler Sequence

R. G. Wilson, V, Letter to N. J. A. Sloane, Sep. 1992

Maple

f:=proc(n) if n mod 2 = 0 then RETURN(round(sqrt(n))) else RETURN(round(n^(3/2))); fi; end; # corrected by R. J. Mathar, Jul 28 2007

Mathematica

mjs[n_] := If[EvenQ[n], Round[Sqrt[n]], Round[Sqrt[n^3]]]; f[n_] := Length[NestWhileList[mjs, n, # != 1 &]] - 1; Table[ f[n], {n, 90}]

Crossrefs

Cf. A094685, A007320, A094683.

Sequence in context: A215578 A007320 A199734 * A062828 A124457 A258102

Adjacent sequences: A007318 A007319 A007320 * A007322 A007323 A007324

Keyword

nonn,easy

Author

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

Extensions

More terms from N. J. A. Sloane, Jun 09 2004

Status

approved