Let P be an odd prime, denote by p(n) (q(n)) the n(th) prime not equal
P with (Pn/P) = 1(= -1), d(n) = q(n) = p(n). We discuss the question
whether d(n) changes sign infinitely often or not. Without using Turan
's power sum method the following theorem is proved. Suppose that the
L-function L(s, chi), defined by the real primitive character mod P, h
as no real root sigma with 1/2 < sigma < 1. Then the numbers d(n) chan
ge sign infinitely often. The hypothesis is known to be true for all P
with 2 < P less than or equal to 227 (J. B. Rosser. J. of Research of
the Nat. Bureau of Standards 45, 505-514 (1950)).