  We show that there exist non-Koszul graded algebras that appear to be Koszul
up to any given cohomological degree. For any integer m>2 we exhibit a
non-commutative quadratic algebra for which the corresponding bigraded Yoneda
algebra is generated in degrees (1,1) and (m,m+1). The algebra is therefore not
Koszul but is m-Koszul (in the sense of Backelin). These examples answer a
question of Green and Marcos.
