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A094698 Number of steps where the Juggler sequence reaches a new record. 4
0, 1, 6, 7, 9, 11, 17, 19, 43, 73, 75, 80, 88, 96, 107, 131, 166, 193, 201, 258, 263, 268, 271, 298, 335, 340, 443, 479, 484 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Records in A007320.

The Juggler sequence: begin with x; if x is even, floor(sqrt(x)) -> x; if x is odd, floor(sqrt(x^3)) -> x; repeat until x = 1, count the iterations.

LINKS

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Juggler Sequence

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]; Print[n]], {n, 3053595}] (* Robert G. Wilson v, Jun 14 2004 *)

CROSSREFS

Cf. A007320, A094670, A094679.

Sequence in context: A240882 A241266 A095908 * A096405 A228499 A309961

Adjacent sequences:  A094695 A094696 A094697 * A094699 A094700 A094701

KEYWORD

nonn,more,hard

AUTHOR

N. J. A. Sloane, Jun 09 2004

EXTENSIONS

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

a(25) = 335 from Eric W. Weisstein, Jan 25 2006

Edited by N. J. A. Sloane, Sep 16 2008 at the suggestion of Tim Nikkel

a(26)-a(29) from Giovanni Resta, Apr 08 2017

STATUS

approved

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Last modified July 29 08:46 EDT 2021. Contains 346340 sequences. (Running on oeis4.)