  For Jacobi matrices with a_n = 1+(-1)^n alpha n^{-gamma}, b_n = (-1)^n beta
n^{-gamma}, we study bound states and the SzegHo condition. We provide a new
proof of Nevai's result that if gamma > 1/2, the Szego condition holds, which
works also if one replaces (-1)^n by cos(mu n). We show that if alpha = 0, beta
not equal to 0, and gamma < 1/2, the Szego condition fails. We also show that
if gamma = 1, alpha and beta are small enough (beta^2 + 8 alpha^2 < 1/24 will
do), then the Jacobi matrix has finitely many bound states (for alpha = 0, beta
large, it has infinitely many).
