

A094670


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


8



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
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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: A097542 A277850 A217291 * 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



