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 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). 3

%I #18 Jan 25 2014 16:39:17

%S -7,-8,-4,-3,-8,-4,-4,-8,-20,-4,-3,-4,-4,-8,-20,-4,-8,-4,-8,-7,-4,-3,

%T -8,-4,-4,-4,-3,-8,-4,-4,-3,-8,-4,-8,-4,-3,-4,-8,-20,-4,-8,-4,-7,-4,

%U -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

%N 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).

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

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

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

%Y Cf. A088192, A220861, A220862.

%K sign

%O 1,1

%A _N. J. A. Sloane_, Dec 26 2012

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Last modified September 15 22:11 EDT 2024. Contains 375959 sequences. (Running on oeis4.)