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

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

Author

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

Keywords

• nonn
• easy

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

Crossrefs

Cf. A094685, A007320, A094683.

Programs

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}]

Extensions

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