A094670 Smallest number which requires n iterations to reach 1 in the juggler sequence problem.

1, 2, 4, 16, 7, 5, 3, 9, 33, 19, 81, 25, 353, 183, 39, 201, 103, 37, 205, 77, 681, 263, 3817, 429, 175, 1673, 539, 165, 671, 321, 5875, 477, 173, 2243, 265, 29017, 1011, 677, 9361, 659, 241, 3389, 1123, 163, 2057, 625, 15271, 4481

Offset

0,2

Comments

A juggler sequence is defined as follows: given a positive integer x, repeat: if x is even then x <- [x^(1/2)] else x <- [x^(3/2)] until x=1. The brackets indicate the floor function.

a(104) is unknown ( > 10000000). - Robert G. Wilson v, Jun 11 2014

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..103

Eric Weisstein's World of Mathematics, Juggler Sequence

Robert G. Wilson v, List of n & a(n) for  n = 0..450 (with 0's for unknown entries)

Mathematica

js[n_] := If[ EvenQ[ n], Floor[ Sqrt[n]], Floor[ Sqrt[n^3]]]; f[n_] := Length[ NestWhileList[js, n, # != 1 &]] - 1; a = Table[0, {50}]; Do[ b = f[n]; If[b < 51 && a[[b]] == 0, a[[b]] = n; Print[n, " = ", b]], {n, 10^5}] (* Robert G. Wilson v *)

Crossrefs

Cf. A007320, A094679, A094698.

Sequence in context: A364247 A338839 A350554 * A110005 A019540 A109584

Adjacent sequences: A094667 A094668 A094669 * A094671 A094672 A094673

Keyword

nonn

Author

Jason Earls, Jun 09 2004

Extensions

More terms from Robert G. Wilson v, Jun 14 2004

Status

approved