A094698 Number of steps where the Juggler sequence reaches a new record.

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

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 * A361419 A096405 A228499

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