Integer sequences having prescribed quadratic character

For the odd primes p, = 3, p2 = 5, ■ • -, we determine integer sequences Np such that the Legendre symbol (N/p,) = +1 for all pi S P for a prescribed array of signs ± 1; (i.e., for a prescribed quadratic character). We examine six quadratic characters having special interest and applications. We present tables of these Np and examine some applications, particularly to questions concerning extreme values for the smallest primitive root (of a prime N), the class number of the quadratic field R(J — N), the real Dirichlet L functions, and quadratic character sums.

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