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 2009-10-15 12:24:52