Color each of the numbers 1 through n either red or blue such that if a+b=c then a, b and c are not all the same color. The addends are distinct.
For example with n=6 the sequence
rbrbrb does not work because 2+4=6 but are all blue.
Whereas rbrbbr does work.
What is the largest value of n for which such a sequence exists?
Note: Since the colors can be swapped, make the number 1 red.
Add a third color (green.) What is the new maximum value of n?
(In reply to
re(2): Sloane says by Charlie)
BTW, the first n=52 found for 4 colors is
rrbrbbrggrgbrbgrygrybrbyryyrybrbyryyrybrbgrggrgbgbrb
I'll see if the program, if left running long enough, can get closer to Sloane's n=66.

Posted by Charlie
on 20091015 12:24:52 