A220863 Choose smallest m>0 such that the n-th rational prime p splits in the imaginary quadratic extension field K = Q(sqrt(-m)); a(n) = discriminant(K).

-7, -8, -4, -3, -8, -4, -4, -8, -20, -4, -3, -4, -4, -8, -20, -4, -8, -4, -8, -7, -4, -3, -8, -4, -4, -4, -3, -8, -4, -4, -3, -8, -4, -8, -4, -3, -4, -8, -20, -4, -8, -4, -7, -4, -4, -3, -8, -3, -8, -4, -4, -7, -4, -8, -4, -20, -4, -3, -4, -4, -8, -4, -8, -11, -4, -4, -8, -4, -8, -4, -4, -7, -3, -4, -8

Offset: 1

Author

N. J. A. Sloane, Dec 26 2012

Keywords

• sign

Comments

a(n) = discriminant of extension field defined in A220862.

References

• David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, Cor. 5.17, p. 105.

Crossrefs

Cf. A088192, A220861, A220862.

Formula

Let i = A220862(n). Then a(n) = i if i == 1 (mod 4), otherwise 4i.