A143742 - OEIS

%I #11 Feb 16 2025 08:33:08

%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="https://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

%O 1,2

%A _Harry J. Smith_, Oct 06 2008

%E Comment clarified by _Harvey P. Dale_, Dec 21 2024