login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I #27 Jan 25 2014 16:39:17

%S -4,-3,-20,-7,-11,-52,-68,-19,-23,-116,-31,-148,-164,-43,-47,-212,-59,

%T -244,-67,-71,-292,-79,-83,-356,-388,-404,-103,-107,-436,-452,-127,

%U -131,-548,-139,-596,-151,-628,-163,-167,-692,-179,-724,-191,-772,-788,-199

%N 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).

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

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

%H Bruno Berselli, <a href="/A220861/b220861.txt">Table of n, a(n) for n = 1..1000</a>

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

%Y Cf. A088192, A220862, A220863.

%K sign

%O 1,1

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 27 10:11 EDT 2024. Contains 375468 sequences. (Running on oeis4.)