Definition: A word w in the alphabet {0,1} is a (k,D) Parisi word if w^infin\ ity avoids arithmetial pprogressions of 1s of length k up to spacing D These are all words cup to circular rotation Let's take k=3 D=1 {[0, 1, 1]} D=2 {[0, 1, 1]} D=3 {[0, 0, 1, 1]} D=3 {[0, 0, 1, 1]} D=4 {[0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 0, 0 , 1, 1]} D=5 {[0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 0, 0 , 1, 1]} D=6 {[0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 0, 0 , 1, 1]} D=7 {[0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 0, 0 , 1, 1]} D=8 {[0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 1, 0, 1, 0, 0 , 1, 1]} D=9 {[0, 0, 0, 0, 0, 1, 1, 0, 1, 1]} D=10 {[0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0 , 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 1 , 0, 0, 1, 0, 1]} D=11 {[0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1], [0 , 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1], [0, 0 , 0, 1, 0, 0, 1, 0, 0, 0, 1, 1], [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1]} D=13 {[0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]} ------------------------- This took, 1720.969, seconds.