A143745 The next largest juggler number.

1, 2, 36, 140, 52214, 24906114455136, 202924588924125339424550328

Offset: 1

Author

Harry J. Smith, Oct 08 2008

Keywords

• nonn

Comments

The juggler sequence: begin with a starting value x and if x is even, x <- floor(sqrt(x)) and if x is odd, x <- floor(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.

Examples

			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.
		

References

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

Links

• 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

Crossrefs

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