%I #21 Dec 15 2017 17:36:39
%S 1,2,3,9,19,25,37,77,163,193,1119,1155,4065,4229,4649,7847,13325,
%T 34175,59739,78901,636731,1122603,1301535,2263913,5947165,72511173,
%U 78641579,125121851,198424189
%N n sets a new record for number of iterations to reach 1 in the juggler sequence problem.
%C Where records occur in A007320.
%C The Juggler sequence: begin with x and if x is even, [sqrt(x)] -> x and if x is odd, [sqrt(x^3)] -> x and repeat until x = 1, count the iterations. - _Robert G. Wilson v_, Jun 14 2004
%C 78901 reaches a maximum of 4064983429...(skip the next 371727 digits)...2140697134 during its trip to 1. - _Robert G. Wilson v_, Jun 14 2004
%C I postulate that 2 is the only even number in this sequence. - _Harry J. Smith_, Aug 15 2008
%C a(30) > 1.6*10^9. - _Giovanni Resta_, Apr 08 2017
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JugglerSequence.html">Juggler Sequence</a>
%e 78901 takes 258 iterations to reach 1; see A094698 for the others.
%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]], {n, 3053595}]; a (* _Robert G. Wilson v_ *)
%Y Cf. A007320, A094670, A094698, A095906, A094698.
%K more,nonn,hard
%O 1,2
%A _Jason Earls_, Jun 09 2004
%E More terms from _Robert G. Wilson v_, Jun 14 2004
%E a(25) = 5947165 from _Eric W. Weisstein_, Jan 25 2006
%E a(26)-a(27) from _Robert G. Wilson v_, Jun 15 2014
%E a(28)-a(29) from _Giovanni Resta_, Apr 08 2017