OFFSET
1,1
COMMENTS
Negatives of odd fundamental discriminants D := b^2-4*a*c<0 of definite integer binary quadratic forms F=a*x^2+b*x*y+c*y^2. See Buell reference pp. 224-230. See 4*A089269 = A191483 for the even case and A003657 for combined even and odd numbers. - Wolfdieter Lang, Nov 07 2003
The asymptotic density of this sequence is 2/Pi^2 = 0.202642... (A185197). - Amiram Eldar, Feb 10 2021
REFERENCES
Richard A. Mollin, Quadratics, CRC Press, 1996, Tables B1-B3.
Duncan A. Buell, Binary Quadratic Forms, Springer-Verlag, NY, 1989.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
A. M. Legendre, Diviseurs de la forme t^2+au^2 a étant un nombre de la forme 4n-1, Essai sur la Théorie des Nombres An VI, Table V.
MATHEMATICA
fQ[n_] := SquareFreeQ[n] && Mod[n, 4] == 3; Select[ Range@ 258, fQ] (* Robert G. Wilson v, Mar 02 2011 *)
Select[Range[3, 300, 4], SquareFreeQ] (* Harvey P. Dale, Mar 08 2015 *)
PROG
(Magma) [4*n+3: n in [0..63] | IsSquarefree(4*n+3)]; // Bruno Berselli, Mar 04 2011
(Haskell)
a039957 n = a039957_list !! (n-1)
a039957_list = filter ((== 3) . (`mod` 4)) a005117_list
-- Reinhard Zumkeller, Aug 15 2011
(PARI) is(n)=n%4==3 && issquarefree(n) \\ Charles R Greathouse IV, Feb 07 2017
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Offset corrected
STATUS
approved