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, 527

Offset: 1

Author

N. J. A. Sloane, Jun 09 2004

Keywords

• nonn
• more
• hard

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

• Eric Weisstein's World of Mathematics, Juggler Sequence

Crossrefs

Cf. A007320, A094670, A094679.

Programs

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 *)

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

a(30) from Ethan Slota, Apr 15 2025