A143742 Starting values that produce a larger juggler number than smaller starting values.

1, 2, 3, 9, 25, 37, 113, 173, 193, 2183, 11229, 15065, 15845, 30817, 48443, 275485, 1267909, 2264915, 5812827, 7110201

Offset: 1

Author

Harry J. Smith, Oct 06 2008

Keywords

• nonn

Comments

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.

Examples

			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.
		

References

• C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 233.

Links

• Eric Weisstein's World of Mathematics, Juggler Sequence
• H. J. Smith, Juggler Sequence

Crossrefs

Cf. A007320, A094670, A094679, A094683, A094684, A095908.

Programs

Mathematica

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 *)

Extensions

Comment clarified by Harvey P. Dale, Dec 21 2024