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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 19 15:57 EDT 2021. Contains 345144 sequences. (Running on oeis4.)