A033197 Discriminants of quadratic number fields Q(sqrt -n) for n squarefree.

-4, -8, -3, -20, -24, -7, -40, -11, -52, -56, -15, -68, -19, -84, -88, -23, -104, -116, -120, -31, -132, -136, -35, -148, -152, -39, -164, -168, -43, -184, -47, -51, -212, -55, -228, -232, -59, -244, -248, -260, -264, -67, -276, -280, -71, -292, -296, -308, -312, -79, -328, -83, -340, -344, -87, -356

Offset

1,1

References

David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989, p. 103.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

For n squarefree and negative, a(n) = n if n == 1 (mod 4), otherwise a(n) = 4n.

Mathematica

max = 56; j = 1; Do[ If[ SquareFreeQ[n], v[j] = n; j = j+1], {n, 1, 2*max}]; Do[ a[n] = -v[n]*If[Mod[v[n], 4] == 3, 1, 4], {n, 1, j-1}]; Table[a[n], {n, 1, max}] (* Jean-François Alcover, Oct 18 2011, after PARI *)

Prog

(PARI) bnd = 1000; L = vector(bnd); j = 1; for (i=1, bnd, if(issquarefree(i), L[j]=i:j=j+1)); M = vector(j-1); for (i=1, j-1, M[i]=if((L[i]%4==3), -L[i], -4*L[i])); M

Crossrefs

Values of n run through A005117. See A000924 for class numbers of these fields.

Sequence in context: A066199 A103647 A372356 * A124002 A014457 A365941

Adjacent sequences: A033194 A033195 A033196 * A033198 A033199 A033200

Keyword

sign,easy,nice

Author

N. J. A. Sloane

Status

approved