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

1,2

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.

References

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

Links

Table of n, a(n) for n=1..20.

Eric Weisstein's World of Mathematics, Juggler Sequence

H. J. Smith, Juggler Sequence

Example

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.

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 *)

Crossrefs

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

Sequence in context: A318231 A242271 A056198 * A038523 A358410 A361863

Adjacent sequences: A143739 A143740 A143741 * A143743 A143744 A143745

Keyword

nonn

Author

Harry J. Smith, Oct 06 2008

Extensions

Comment clarified by Harvey P. Dale, Dec 21 2024

Status

approved