And what about the number of integer values taken by : x x^x, x^x^x, x^x^x^x using parentheses as desired when x=sqrt(2) , x=2^(1/3) ..... when x=sqrt(2) n=3 there is a well known example : (sqrt(2)^sqrt(2))^sqrt(2)=sqrt(2)^(sqt(2)*sqrt(2))=sqrt(2)^2=2 integer hence a(1)=0 a(2)=0 a(3)=1 a(4)>=1... Benoit Cloitre abcloitre at wanaddo.fr