A220861 Choose smallest m>0 such that the n-th rational prime p ramifies in the imaginary quadratic extension field K = Q(sqrt(-m)); a(n) = discriminant(K).

-4, -3, -20, -7, -11, -52, -68, -19, -23, -116, -31, -148, -164, -43, -47, -212, -59, -244, -67, -71, -292, -79, -83, -356, -388, -404, -103, -107, -436, -452, -127, -131, -548, -139, -596, -151, -628, -163, -167, -692, -179, -724, -191, -772, -788, -199

Offset: 1

Author

N. J. A. Sloane, Dec 26 2012

Keywords

• sign

Comments

m=1 if p=2, otherwise m=p.

References

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

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A088192, A220862, A220863.

Formula

Let p = prime(n). Then a(n) = -4 if p = 2, -p if p == 3 mod 4, -4p if p == 1 mod 4.