A094679 n sets a new record for number of iterations to reach 1 in the juggler sequence problem.

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

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