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

Author

Jason Earls, Jun 09 2004

Keywords

• nonn

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)

Crossrefs

Cf. A007320, A094679, A094698.

Programs

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 *)

Extensions

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