OFFSET
0,2
COMMENTS
Removing all such intervals (without an upper limit on n) leaves a nowhere dense subset of [0,1]. However, since each step removes additional points of measure no more than 1/2^(n+1), this nowhere dense subset must make up at least half of [0,1] and so be of positive measure. In fact its measure is 0.535573680435778224753342807..., the limit of a(n)/A000302(n).
FORMULA
a(n) = 4*a(n-1)-A045690(n) for n>0. a(2n+2)=6*a(2n+1)-8*a(2n); a(4n+3)=6*a(4n+2)-8*a(4n+1)+a(n); a(4n+5)=6*a(4n+4)-8*a(4n+3)+2*a(n).
a(n) = A045690(2n+2). a(2n+1)=4*a(2n)-a(n); a(2n+2)=4*a(2n+1)-2*a(n). - Mamuka Jibladze, Sep 30 2014
EXAMPLE
At the start the interval [0,1] has measure 1=1/1. The first step removes the interval [3/8,5/8], leaving a subset with a measure of 3/4. The second step in addition removes the intervals [7/32,9/32] and [23/32,25/32], leaving a subset with a measure of 5/8=10/16. The third step in addition removes the intervals [15/128,17/128], [47/128,3/8), (5/8,81/128] and [111/128,113/128], leaving a subset with a measure of 37/64.
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Apr 25 2005
STATUS
approved