OFFSET
0,2
COMMENTS
The player begins with x=1/2, and wins or loses min(x/2,(1-x)/2) at each step.
After step n, the player has x=d/2^(n+1), where d is an odd number between 0 and 2^(n+1).
How dense are the numbers at level n of the Zeno tree, as a proportion of the 2^n numbers that might be there? This data suggests that the density scales by about 0.72 at each step.
(The 45/128,83/128 near the bottom of the lower figure on p. 196 of Hayes (2008) should be 47/128,81/128.)
LINKS
Brian Hayes, Follow the money, American Scientist 90:400-405, 2002.
Brian Hayes, Wagering with Zeno, American Scientist, May/June 2008, pp. 194-199.
EXAMPLE
a(1)=2 because {1/4,3/4} are possible outcomes after 1 step.
a(2)=4 because {1/8,3/8,5/8,7/8} are possible after 2 steps.
a(3)=6 because {1,3,7,9,13,15}/16 are possible after 3 steps.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Apr 21 2008
EXTENSIONS
a(8) corrected and a(11)-a(40) from Andrew Howroyd, Oct 16 2017
Edited and further extended by Don Reble, Oct 17 2017
STATUS
approved