A039957 Squarefree numbers congruent to 3 mod 4.

3, 7, 11, 15, 19, 23, 31, 35, 39, 43, 47, 51, 55, 59, 67, 71, 79, 83, 87, 91, 95, 103, 107, 111, 115, 119, 123, 127, 131, 139, 143, 151, 155, 159, 163, 167, 179, 183, 187, 191, 195, 199, 203, 211, 215, 219, 223, 227, 231, 235, 239, 247, 251, 255

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

Cf. A039955, A039956, A185197, A191483.

Sequence in context: A118894 A194397 A330213 * A217332 A369056 A079422

Adjacent sequences: A039954 A039955 A039956 * A039958 A039959 A039960

Keyword

nonn,easy,nice

Author

R. K. Guy

Extensions

Offset corrected

Status

approved