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%I #10 Dec 21 2024 11:50:39
%S 1,2,3,9,25,37,113,173,193,2183,11229,15065,15845,30817,48443,275485,
%T 1267909,2264915,5812827,7110201
%N Starting values that produce a larger juggler number than smaller starting values.
%C The juggler sequence: begin with a starting value x and if x is even, x -> [sqrt(x)] and if x is odd, x -> [sqrt(x^3)] and repeat until x = 1, save the starting value, max x and the number of steps needed to reach it.
%D C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 233.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JugglerSequence.html">Juggler Sequence</a>
%H H. J. Smith, <a href="http://harry-j-smith-memorial.com/Juggler/JuggWhat.html">Juggler Sequence</a>
%e 37 is in the sequence because starting at 37 the juggler sequences maxes out at 24906114455136, a 14-digit number, after 8 steps. This is the largest juggler number found for starting values less than or equal to 37.
%t DeleteDuplicates[Table[{n,Max[NestWhileList[If[EvenQ[#],Floor[Sqrt[#]],Floor[Sqrt[#^3]]]&,n,#!=1&]]},{n,50000}],GreaterEqual [#1[[2]],#2[[2]]]&][[;;,1]] (* The program generates the first 15 terms of the sequence. *) (* _Harvey P. Dale_, Dec 21 2024 *)
%Y Cf. A007320, A094670, A094679, A094683, A094684, A095908.
%K nonn,changed
%O 1,2
%A _Harry J. Smith_, Oct 06 2008
%E Comment clarified by _Harvey P. Dale_, Dec 21 2024