1,2

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.

I have a b-file for this sequence for n=1,...,19 (all known values), but some a(n) values are much larger than 1000 digits.

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

Harry J. Smith, Table of n, a(n) for n = 1..9

H. J. Smith, Juggler Sequence

Eric Weisstein's World of Mathematics, Juggler Sequence

24906114455136 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.

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

Sequence in context: A069067 A145450 A134785 this_sequence A007757 A141217 A025531

Adjacent sequences: A143742 A143743 A143744 this_sequence A143746 A143747 A143748

nonn

Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 08 2008