

A094679


n sets a new record for number of iterations to reach 1 in the juggler sequence problem.


7



1, 2, 3, 9, 19, 25, 37, 77, 163, 193, 1119, 1155, 4065, 4229, 4649, 7847, 13325, 34175, 59739, 78901, 636731, 1122603, 1301535, 2263913, 5947165, 72511173, 78641579, 125121851, 198424189
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OFFSET

1,2


COMMENTS

Where records occur in A007320.
The Juggler sequence: begin with x and if x is even, [sqrt(x)] > x and if x is odd, [sqrt(x^3)] > x and repeat until x = 1, count the iterations.  Robert G. Wilson v, Jun 14 2004
78901 reaches a maximum of 4064983429...(skip the next 371727 digits)...2140697134 during its trip to 1.  Robert G. Wilson v, Jun 14 2004
I postulate that 2 is the only even number in this sequence.  Harry J. Smith, Aug 15 2008
a(30) > 1.6*10^9.  Giovanni Resta, Apr 08 2017


LINKS

Table of n, a(n) for n=1..29.
Eric Weisstein's World of Mathematics, Juggler Sequence


EXAMPLE

78901 takes 258 iterations to reach 1; see A094698 for the others.


MATHEMATICA

$MaxPrecision = 250000000; js[n_] := If[ EvenQ[ n], Floor[ Sqrt[n]], Floor[ Sqrt[n^3]]]; f[n_] := Block[{c = 1, k = n}, While[k = js[k]; k != 1, c++ ]; c]; a = {0}; Do[ b = f[n]; If[b > a[[ 1]], AppendTo[a, b]], {n, 3053595}]; a (* Robert G. Wilson v *)


CROSSREFS

Cf. A007320, A094670, A094698, A095906, A094698.
Sequence in context: A298347 A113201 A089753 * A298357 A094812 A307898
Adjacent sequences: A094676 A094677 A094678 * A094680 A094681 A094682


KEYWORD

more,nonn,hard


AUTHOR

Jason Earls, Jun 09 2004


EXTENSIONS

More terms from Robert G. Wilson v, Jun 14 2004
a(25) = 5947165 from Eric W. Weisstein, Jan 25 2006
a(26)a(27) from Robert G. Wilson v, Jun 15 2014
a(28)a(29) from Giovanni Resta, Apr 08 2017


STATUS

approved



