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

1,1

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.

Links

Table of n, a(n) for n=1..75.

Formula

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

Crossrefs

Cf. A088192, A220861, A220862.

Sequence in context: A359009 A092157 A220351 * A330161 A197823 A011243

Adjacent sequences: A220860 A220861 A220862 * A220864 A220865 A220866

Keyword

sign

Author

N. J. A. Sloane, Dec 26 2012

Status

approved