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Number of steps where the Juggler sequence reaches a new record.
4

%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