shoelaces and aglets

[N. J. A. Sloane]

I rewrote the description, but in view of Jack B.'s comment,
further changes may be needed.  Here is what will appear in the OEDIS
in about 10 minutes:

%I A106744
%S A106744 1,2,2,3,3,4,5,6,6,7,8,9,10,11,11,12,13,14,15
%N A106744 Given n shoelaces, each with two aglets; sequence gives number of ag\
let pairs that must be picked up to guarantee that the probability that none re\
main is > 1/2.
%C A106744 Assistance in extending sequence given by Gerald McGarvey (Gerald.Mc\
Garvey(AT)comcast.net)
%e A106744 a(2)=2 because given 2 shoelaces, p=1/3 that the first two aglets pi\
cked up will be on a single shoelace, requiring another pick-up, and p=2/3 that\
 they won't, so the mean no. of pick-ups is (1/3)*2 + (2/3)*1 = 4/3, for which \
the ceiling is 2.
%O A106744 1,2
%K A106744 nonn
%A A106744 N Fernandez (primeness(AT)borve.demon.co.uk), May 16 2005

NJAS