%I #23 Jan 16 2019 02:40:50
%S 0,1,6,7,9,11,17,19,43,73,75,80,88,96,107,131,166,193,201,258,263,268,
%T 271,298,335,340,443,479,484
%N Number of steps where the Juggler sequence reaches a new record.
%C Records in A007320.
%C 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.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JugglerSequence.html">Juggler Sequence</a>
%t $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 *)
%Y Cf. A007320, A094670, A094679.
%K nonn,more,hard
%O 1,3
%A _N. J. A. Sloane_, Jun 09 2004
%E More terms from _Robert G. Wilson v_, Jun 14 2004
%E a(25) = 335 from _Eric W. Weisstein_, Jan 25 2006
%E Edited by _N. J. A. Sloane_, Sep 16 2008 at the suggestion of Tim Nikkel
%E a(26)-a(29) from _Giovanni Resta_, Apr 08 2017